2.4.23 second order ode constant coeff using laplace

Table 2.495: second order ode constant coeff using laplace

#

ODE

CAS classification

Solved?

530

\[ {}x^{\prime \prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

531

\[ {}x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

532

\[ {}x^{\prime \prime }-x^{\prime }-2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

533

\[ {}x^{\prime \prime }+8 x^{\prime }+15 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

534

\[ {}x^{\prime \prime }+x = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

535

\[ {}x^{\prime \prime }+4 x = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

536

\[ {}x^{\prime \prime }+x = \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

537

\[ {}x^{\prime \prime }+9 x = 1 \]
i.c.

[[_2nd_order, _missing_x]]

538

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 1 \]
i.c.

[[_2nd_order, _missing_x]]

539

\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

541

\[ {}x^{\prime \prime }+6 x^{\prime }+25 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

542

\[ {}x^{\prime \prime }-6 x^{\prime }+8 x = 2 \]
i.c.

[[_2nd_order, _missing_x]]

543

\[ {}x^{\prime \prime }-4 x = 3 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

544

\[ {}x^{\prime \prime }+4 x^{\prime }+8 x = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

551

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = t \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

552

\[ {}x^{\prime \prime }+6 x^{\prime }+18 x = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

553

\[ {}x^{\prime \prime }+9 x = 6 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

554

\[ {}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25} = 6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

561

\[ {}x^{\prime \prime }+4 x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

562

\[ {}x^{\prime \prime }+2 x^{\prime }+x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

563

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

564

\[ {}x^{\prime \prime }+4 x = \delta \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

565

\[ {}x^{\prime \prime }+4 x = \delta \left (t \right )+\delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

566

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 1+\delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

567

\[ {}x^{\prime \prime }+2 x^{\prime }+x = t +\delta \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

568

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

569

\[ {}x^{\prime \prime }+9 x = \delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

570

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = \delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

571

\[ {}x^{\prime \prime }+2 x^{\prime }+x = \delta \left (t \right )-\delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

572

\[ {}x^{\prime \prime }+4 x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

573

\[ {}x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

574

\[ {}x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

575

\[ {}x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1483

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1484

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1485

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1486

\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1487

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1490

\[ {}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1491

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1492

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1493

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1494

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1495

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1496

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1497

\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1498

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1499

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1500

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1501

\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1503

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1504

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1505

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1506

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1507

\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1508

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1509

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1510

\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1511

\[ {}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1512

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1514

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1515

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1516

\[ {}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1518

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2671

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2672

\[ {}2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2673

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2674

\[ {}y^{\prime \prime }+y = t^{2} \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2675

\[ {}y^{\prime \prime }+3 y^{\prime }+7 y = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2676

\[ {}y^{\prime \prime }+y^{\prime }+y = t^{3} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2678

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2679

\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2680

\[ {}y^{\prime \prime }+y = t \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2681

\[ {}y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2682

\[ {}y^{\prime \prime }-2 y^{\prime }+7 y = \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2683

\[ {}y^{\prime \prime }+y^{\prime }+y = 1+{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2684

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2685

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2686

\[ {}y^{\prime \prime }+y^{\prime }+y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2687

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2688

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2689

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2690

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2691

\[ {}y^{\prime \prime }+y^{\prime }+7 y = \left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2692

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2693

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2694

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2695

\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )+\delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2696

\[ {}y^{\prime \prime }+y^{\prime }+y = 2 \delta \left (t -1\right )-\delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2697

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}+3 \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3935

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3936

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3937

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \]
i.c.

[[_2nd_order, _missing_x]]

3938

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \]
i.c.

[[_2nd_order, _missing_x]]

3939

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3940

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3941

\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \]
i.c.

[[_2nd_order, _missing_y]]

3942

\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3943

\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3944

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3945

\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3946

\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3947

\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3948

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3949

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3950

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3951

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3952

\[ {}y^{\prime \prime }+4 y = 9 \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3953

\[ {}y^{\prime \prime }+y = 6 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3954

\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3955

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3963

\[ {}y^{\prime \prime }-y = \operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3964

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3965

\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3966

\[ {}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3967

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3968

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-t +1} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3969

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3970

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3977

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3978

\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3979

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3980

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3981

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3982

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3983

\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3984

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3985

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4514

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4515

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

4516

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

4517

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4518

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4519

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 8 \,{\mathrm e}^{-t} \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4520

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4521

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4522

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4523

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4524

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4525

\[ {}y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4526

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4527

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4528

\[ {}y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6546

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6547

\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6548

\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

6549

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6550

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6551

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6552

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

6553

\[ {}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6557

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6558

\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7349

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7350

\[ {}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7351

\[ {}y^{\prime \prime }-\frac {y}{4} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7352

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7353

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7354

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7355

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7356

\[ {}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7357

\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64 \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7358

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7360

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7361

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7362

\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7363

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7364

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7365

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7366

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7367

\[ {}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7368

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7369

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7370

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7371

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7372

\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7373

\[ {}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7374

\[ {}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7375

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7376

\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7377

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7378

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7379

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7380

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7381

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8167

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8168

\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8169

\[ {}y^{\prime \prime }-y = t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8173

\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

8174

\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{-t +\pi } \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8175

\[ {}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8176

\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8177

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

8178

\[ {}y^{\prime \prime }+3 y^{\prime }+3 y = 2 \]

[[_2nd_order, _missing_x]]

8179

\[ {}y^{\prime \prime }+y^{\prime }+2 y = t \]

[[_2nd_order, _with_linear_symmetries]]

8180

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8181

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8328

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8329

\[ {}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _missing_y]]

8330

\[ {}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8331

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8335

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8338

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8339

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8340

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8341

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8342

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8343

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8344

\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8345

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8346

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8347

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8351

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8352

\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8353

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8354

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8355

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (-4+t \right )+\operatorname {Heaviside}\left (t -6\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8358

\[ {}y^{\prime \prime }+9 y = \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8359

\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8360

\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8361

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8364

\[ {}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8367

\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8368

\[ {}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8369

\[ {}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8370

\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8371

\[ {}y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _missing_y]]

8372

\[ {}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _missing_y]]

8373

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8374

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8375

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8376

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8377

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8378

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8978

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13107

\[ {}x^{\prime \prime }-x^{\prime }-6 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13108

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13109

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13110

\[ {}x^{\prime \prime }-x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13111

\[ {}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13112

\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13113

\[ {}x^{\prime \prime }-2 x = 1 \]
i.c.

[[_2nd_order, _missing_x]]

13115

\[ {}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13118

\[ {}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (-t +1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13119

\[ {}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13120

\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13122

\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13123

\[ {}x^{\prime \prime }+x = \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13124

\[ {}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13125

\[ {}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13126

\[ {}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13127

\[ {}x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13567

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13568

\[ {}y^{\prime \prime }+y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13569

\[ {}y^{\prime \prime }+4 y = 8 \]
i.c.

[[_2nd_order, _missing_x]]

13570

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13571

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13572

\[ {}y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13573

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13574

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13577

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13578

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13579

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13580

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13581

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13582

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13940

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13941

\[ {}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13942

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13943

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13944

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13945

\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13946

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13947

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13948

\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13949

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13950

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13952

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13953

\[ {}y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13954

\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13955

\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13956

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13957

\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13958

\[ {}y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13966

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13967

\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13968

\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13969

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13970

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13971

\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13972

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13973

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +2 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13975

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13976

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13977

\[ {}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13979

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13982

\[ {}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13983

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13984

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13985

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13986

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13987

\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13988

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13989

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13990

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _missing_y]]

13991

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13992

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13993

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13994

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13995

\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13996

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13997

\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13998

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13999

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14000

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14443

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

14445

\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14446

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14447

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

14451

\[ {}y^{\prime \prime }-9 y = 2+x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14452

\[ {}y^{\prime \prime }+9 y = 2+x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14453

\[ {}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14454

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14458

\[ {}y^{\prime \prime }+9 y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

14459

\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14460

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14461

\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14462

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14465

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14466

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _missing_y]]

14467

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14468

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14469

\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14470

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14473

\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14474

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14475

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14476

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14477

\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14880

\[ {}y^{\prime \prime }+4 y = 8 \]
i.c.

[[_2nd_order, _missing_x]]

14881

\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14882

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14883

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14884

\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14885

\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (-4+t \right ) \cos \left (-20+5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14886

\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14887

\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14888

\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14889

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14890

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14891

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14892

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14893

\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14894

\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (-4+t \right )\right ) \cos \left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14895

\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14896

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14897

\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14898

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14899

\[ {}y^{\prime \prime }+16 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15509

\[ {}y^{\prime \prime }-4 y = t^{3} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15510

\[ {}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15511

\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15512

\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15513

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15514

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15515

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 7 \]
i.c.

[[_2nd_order, _missing_x]]

15516

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15517

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15520

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15521

\[ {}y^{\prime \prime }+9 y = 27 t^{3} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15522

\[ {}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15523

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15524

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15525

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15526

\[ {}y^{\prime \prime }+8 y^{\prime }+17 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15527

\[ {}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right ) \]
i.c.

[[_2nd_order, _quadrature]]

15528

\[ {}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15529

\[ {}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15530

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15531

\[ {}y^{\prime \prime }+4 y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

15532

\[ {}y^{\prime \prime }+4 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15533

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15534

\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15535

\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15536

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

15537

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15538

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15539

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15540

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15543

\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _quadrature]]

15544

\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _quadrature]]

15545

\[ {}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15547

\[ {}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]
i.c.

[[_2nd_order, _quadrature]]

15548

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15551

\[ {}y^{\prime \prime } = \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _quadrature]]

15552

\[ {}y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (-4+t \right ) \]
i.c.

[[_2nd_order, _quadrature]]

15554

\[ {}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15555

\[ {}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15557

\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right ) \]

[[_2nd_order, _missing_y]]

15558

\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _missing_y]]

15559

\[ {}y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15560

\[ {}y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15561

\[ {}y^{\prime \prime }+y = \delta \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15562

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15563

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15564

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15565

\[ {}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17209

\[ {}x^{\prime \prime } = 0 \]
i.c.

[[_2nd_order, _quadrature]]

17210

\[ {}x^{\prime \prime } = 1 \]
i.c.

[[_2nd_order, _quadrature]]

17211

\[ {}x^{\prime \prime } = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _quadrature]]

17212

\[ {}x^{\prime \prime }+x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17213

\[ {}x^{\prime \prime }+x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17214

\[ {}x^{\prime \prime }-x^{\prime } = 1 \]
i.c.

[[_2nd_order, _missing_x]]

17215

\[ {}x^{\prime \prime }+x = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17216

\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \]
i.c.

[[_2nd_order, _missing_y]]

17217

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 2 \]
i.c.

[[_2nd_order, _missing_x]]

17218

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 4 \]
i.c.

[[_2nd_order, _missing_x]]

17219

\[ {}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _missing_y]]

17220

\[ {}x^{\prime \prime }+x = 2 \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17633

\[ {}y^{\prime \prime }+2 y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17634

\[ {}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17635

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17636

\[ {}6 y^{\prime \prime }+5 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17637

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7 \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17638

\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17639

\[ {}y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17640

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17643

\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17644

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17645

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17646

\[ {}y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17647

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17648

\[ {}y^{\prime \prime }-8 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17649

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17650

\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17651

\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17652

\[ {}y^{\prime \prime }+w^{2} y = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17653

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17654

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17655

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 18 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17670

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17671

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17672

\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17673

\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17674

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17675

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17676

\[ {}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17677

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17678

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17679

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17680

\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17683

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17684

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17685

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17686

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17687

\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17688

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17689

\[ {}y^{\prime \prime }-y = -20 \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17690

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17691

\[ {}y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17692

\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17693

\[ {}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17694

\[ {}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17695

\[ {}2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17696

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17698

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17699

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17700

\[ {}y^{\prime \prime }+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17701

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17702

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17703

\[ {}y^{\prime \prime }+w^{2} y = g \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17704

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17705

\[ {}4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17706

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17707

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17708

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17711

\[ {}\frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17712

\[ {}\frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18374

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18375

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \]
i.c.

[[_2nd_order, _missing_x]]

18376

\[ {}y^{\prime \prime }+y^{\prime } = 3 x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

18377

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18378

\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18382

\[ {}y^{\prime \prime }+a^{2} y = f \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18383

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

18384

\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

18385

\[ {}y^{\prime \prime }-y^{\prime } = t^{2} \]
i.c.

[[_2nd_order, _missing_y]]

18386

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]