5.8.5 Problems 401 to 500

Table 5.607: Third and higher order ode

#

ODE

Mathematica

Maple

4447

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

4448

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

4449

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

4450

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

4451

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0 \]

4452

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

4453

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

4454

\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0 \]

4455

\[ {}y^{\left (6\right )}-64 y = 0 \]

4461

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

4462

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \]

4463

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

4464

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right ) \]

4465

\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right ) \]

4466

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime }+y = 9 \,{\mathrm e}^{2 x} \]

4467

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 48 x \,{\mathrm e}^{x} \]

4468

\[ {}y^{\prime \prime \prime }-3 y^{\prime } = 9 x^{2} \]

4469

\[ {}y^{\left (5\right )}+4 y^{\prime \prime \prime } = 7+x \]

4471

\[ {}y^{\prime \prime \prime \prime }+16 y = 64 \cos \left (2 x \right ) \]

4472

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y = 44 \sin \left (3 x \right ) \]

4473

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+5 y^{\prime }+5 y = 5 \cos \left (2 x \right ) \]

4475

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

4477

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

4478

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

4489

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 15 \sin \left (2 x \right ) \]

4490

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 \sin \left (2 x \right ) \]

4491

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

4492

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 10 \,{\mathrm e}^{x} \sin \left (x \right ) \]

4493

\[ {}y^{\prime \prime \prime }-2 y^{\prime }-4 y = 50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \]

4494

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x} \]

4495

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 32 \,{\mathrm e}^{2 x}+16 x^{3} \]

4496

\[ {}y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y = 72 \,{\mathrm e}^{3 x}+729 x^{2} \]

4511

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

4513

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

4529

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

4530

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right ) \]

4531

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 t^{2} \operatorname {Heaviside}\left (t -2\right ) \]

4532

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

5921

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]

5922

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

5923

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

5924

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

5927

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

5929

\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]

5930

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

5932

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

5933

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

5934

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

5935

\[ {}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

5936

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]

5939

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

5941

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

5942

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

5943

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

5944

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

5949

\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]

6147

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

6148

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

6149

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

6150

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

6210

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

6229

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \]

6389

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

6391

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

6392

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

6512

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

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

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

6534

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

6554

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

6555

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

6556

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

6692

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

6696

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

6702

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

6704

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

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

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

6713

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

6714

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

6715

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

6732

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8 \]

6734

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x} \]

6738

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

6739

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

6742

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

6751

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

6752

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

6775

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

6779

\[ {}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

6780

\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime } = 0 \]

6783

\[ {}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x \]

6784

\[ {}3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x} \]

6785

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

6877

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

6878

\[ {}t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0 \]

6899

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 12 x^{2} \]