5.20.14 Problems 1301 to 1400

Table 5.933: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

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

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

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

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

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

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