4.20.14 Problems 1301 to 1400

Table 4.929: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

6392

\[ {} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]

6393

\[ {} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

6394

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

6395

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

6396

\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]

6397

\[ {} y^{\prime \prime }-y = \cosh \left (x \right ) \]

6479

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 8 \]

6480

\[ {} y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

6481

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

6482

\[ {} y^{\prime \prime }+25 y = 5 x^{2}+x \]

6483

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

6484

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \]

6485

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

6486

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

6487

\[ {} 2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

6488

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

6489

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

6490

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

6491

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

6492

\[ {} y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

6493

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

6494

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x} \]

6495

\[ {} y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1 \]

6496

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

6497

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

6498

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

6499

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

6500

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

6501

\[ {} y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

6502

\[ {} x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

6503

\[ {} y^{\prime \prime } = 3 \sin \left (x \right )-4 y \]

6504

\[ {} \frac {x^{\prime \prime }}{2} = -48 x \]

6505

\[ {} x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]

6506

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

6507

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

6508

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

6509

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

6510

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

6511

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

6512

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

6513

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

6514

\[ {} y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \]

6518

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

6519

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x} \]

6520

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

6521

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

6522

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

6526

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x} \]

6527

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

6528

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \]

6529

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

6530

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

6531

\[ {} x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2} \]

6534

\[ {} y^{\prime \prime \prime \prime } = 5 x \]

6535

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \]

6536

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

6537

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

6538

\[ {} y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

6539

\[ {} y^{\prime \prime }-7 y^{\prime } = -3 \]

6546

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

6547

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

6548

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

6549

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

6550

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

6551

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

6552

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

6553

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

6554

\[ {} y^{\prime \prime \prime }-y = 5 \]

6555

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

6556

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

6557

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

6558

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

6573

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

6575

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

6576

\[ {} y^{\prime \prime }-y = 4-x \]

6577

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

6578

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{x} \left (1-x \right ) \]

6691

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 0 \]

6692

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

6693

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

6694

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

6701

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

6702

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

6703

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

6704

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0 \]

6705

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

6706

\[ {} y^{\prime \prime }+25 y = 0 \]

6707

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0 \]

6708

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

6709

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

6710

\[ {} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \]

6711

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 1 \]

6712

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

6713

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

6714

\[ {} y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5 \]

6715

\[ {} y^{\prime \prime \prime }-4 y^{\prime } = x \]

6716

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \]

6717

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

6718

\[ {} y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x} \]

6719

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