2.2.40 Problems 3901 to 4000

Table 2.81: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

3901

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}-9 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.694

3902

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=5 x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.707

3903

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}-3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.599

3904

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+3 x_{3} \\ x_{2}^{\prime }=-9 x_{1}-3 x_{2}-9 x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.535

3905

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-17 x_{1}-42 x_{3} \\ x_{2}^{\prime }=-7 x_{1}+4 x_{2}-14 x_{3} \\ x_{3}^{\prime }=7 x_{1}+18 x_{3} \end {array}\right ] \]

system_of_ODEs

0.444

3906

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }=8 x_{1}-15 x_{2}+9 x_{3} \end {array}\right ] \]

system_of_ODEs

1.490

3907

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}-6 x_{2}-7 x_{3} \\ x_{2}^{\prime }=-3 x_{1}-3 x_{2}-3 x_{3} \\ x_{3}^{\prime }=7 x_{1}+6 x_{2}+7 x_{3} \end {array}\right ] \]

system_of_ODEs

0.417

3908

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+6 x_{3} \end {array}\right ] \]

system_of_ODEs

0.424

3909

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2}-2 x_{3} \\ x_{2}^{\prime }=-4 x_{1}-5 x_{2}-6 x_{3} \\ x_{3}^{\prime }=4 x_{1}+8 x_{2}+7 x_{3} \end {array}\right ] \]

system_of_ODEs

0.751

3910

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=4 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+4 x_{3} \end {array}\right ] \]

system_of_ODEs

0.420

3911

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ] \]

system_of_ODEs

0.401

3912

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=x_{1} \end {array}\right ] \]

system_of_ODEs

0.358

3913

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+13 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \\ x_{3}^{\prime }=2 x_{3}+4 x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ] \]

system_of_ODEs

0.740

3914

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{4} \\ x_{2}^{\prime }=6 x_{2} \\ x_{3}^{\prime }=-x_{3} \\ x_{4}^{\prime }=2 x_{1}+5 x_{4} \end {array}\right ] \]

system_of_ODEs

0.723

3915

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \end {array}\right ] \]

system_of_ODEs

0.607

3916

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-2 x_{2}+9 t \\ x_{2}^{\prime }=5 x_{1}-2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.582

3917

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \end {array}\right ] \]

system_of_ODEs

0.479

3918

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\ x_{2}^{\prime }=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.873

3919

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2}+x_{3}+t \\ x_{2}^{\prime }=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}-3 x_{3}+1 \end {array}\right ] \]

system_of_ODEs

0.965

3920

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=8 x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.505

3921

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ] \]

system_of_ODEs

0.477

3922

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ] \]

system_of_ODEs

0.584

3923

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1} \\ x_{2}^{\prime }=-4 x_{2} \end {array}\right ] \]

system_of_ODEs

0.323

3924

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \end {array}\right ] \]

system_of_ODEs

0.461

3925

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-7 x_{2} \end {array}\right ] \]

system_of_ODEs

0.556

3926

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-4 x_{2} \end {array}\right ] \]

system_of_ODEs

0.438

3927

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.457

3928

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

[[_linear, ‘class A‘]]

0.447

3929

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

[[_linear, ‘class A‘]]

0.429

3930

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

[[_linear, ‘class A‘]]

0.464

3931

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

[[_linear, ‘class A‘]]

0.365

3932

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

[[_linear, ‘class A‘]]

0.498

3933

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

[[_linear, ‘class A‘]]

0.519

3934

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

[[_linear, ‘class A‘]]

0.543

3935

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

[[_2nd_order, _missing_x]]

0.316

3936

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

[[_2nd_order, _missing_x]]

0.298

3937

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

[[_2nd_order, _missing_x]]

0.250

3938

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

[[_2nd_order, _missing_x]]

0.221

3939

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

[[_2nd_order, _with_linear_symmetries]]

0.341

3940

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

[[_2nd_order, _with_linear_symmetries]]

0.325

3941

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

[[_2nd_order, _missing_y]]

0.324

3942

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

[[_2nd_order, _with_linear_symmetries]]

0.325

3943

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

[[_2nd_order, _with_linear_symmetries]]

0.322

3944

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

[[_2nd_order, _with_linear_symmetries]]

0.349

3945

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.377

3946

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.323

3947

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.391

3948

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.381

3949

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.378

3950

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.370

3951

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.406

3952

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.368

3953

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.336

3954

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.455

3955

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

[[_2nd_order, _missing_x]]

0.181

3956

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

[[_linear, ‘class A‘]]

0.597

3957

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

[[_linear, ‘class A‘]]

0.670

3958

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

[[_linear, ‘class A‘]]

0.821

3959

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

[[_linear, ‘class A‘]]

0.912

3960

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

[[_linear, ‘class A‘]]

0.809

3961

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

[[_linear, ‘class A‘]]

1.102

3962

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

[[_linear, ‘class A‘]]

82.323

3963

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.765

3964

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.080

3965

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.655

3966

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.662

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]]

1.645

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]]

1.299

3969

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.546

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]]

3.938

3971

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

[[_linear, ‘class A‘]]

0.731

3972

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

[[_linear, ‘class A‘]]

0.966

3973

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

[[_linear, ‘class A‘]]

0.504

3974

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

[[_linear, ‘class A‘]]

0.583

3975

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

[[_linear, ‘class A‘]]

0.588

3976

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

[[_linear, ‘class A‘]]

0.695

3977

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.813

3978

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.816

3979

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.958

3980

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.170

3981

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.022

3982

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.178

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]]

0.899

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]]

1.343

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]]

2.024

3986

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

0.368

3987

\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[_erf]

0.349

3988

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.331

3989

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.333

3990

\[ {}y^{\prime \prime }+x y = 0 \]

[[_Emden, _Fowler]]

0.295

3991

\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.327

3992

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.346

3993

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

[[_2nd_order, _with_linear_symmetries]]

0.354

3994

\[ {}\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.387

3995

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.384

3996

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

[_Gegenbauer]

0.405

3997

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

0.334

3998

\[ {}y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.383

3999

\[ {}y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.420

4000

\[ {}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.467