4.23.3 Problems 201 to 300

Table 4.1003: Higher order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

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

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

6738

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

6739

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

6742

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

6775

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

7529

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

7530

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]

7531

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

7534

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

7539

\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

7582

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

7659

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

7660

\[ {} y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

7661

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

7662

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

7663

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

7672

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

7673

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

7984

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

8032

\[ {} y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]

8033

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

8034

\[ {} y^{\prime \prime \prime }-y^{\prime } = 1 \]

8332

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

8333

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

8872

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

9165

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

11428

\[ {} y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2} = 0 \]

11435

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

11436

\[ {} y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x} = 0 \]

11443

\[ {} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0 \]

11499

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

11501

\[ {} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0 \]

11502

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

11506

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0 \]

11508

\[ {} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0 \]

11539

\[ {} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \]

11540

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

11543

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

12858

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

12860

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

12863

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

12865

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

12872

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

12873

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

12874

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

12876

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

12882

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

12884

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

12885

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

12887

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

12890

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

12893

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

13107

\[ {} x^{\prime \prime \prime }+x^{\prime } = 1 \]

13110

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

13388

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \]

13389

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 x \,{\mathrm e}^{-2 x} \]

13390

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \]

13391

\[ {} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \]

13394

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \]

13395

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \]

13396

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

13397

\[ {} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \]

13398

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{x} x -4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \]

13399

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \]

13402

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 \,{\mathrm e}^{x} x +4 \,{\mathrm e}^{3 x}-9 \]

13403

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \]

13418

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}-\sin \left (x \right ) \]

13419

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \]

13425

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

13426

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

13427

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]

13428

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \]

13429

\[ {} y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right ) \]

13430

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

13431

\[ {} y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \]

13432

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

13433

\[ {} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (2 x \right ) \sin \left (x \right ) \]

13459

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

13583

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right ) \]

13584

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t} \]

13709

\[ {} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

13710

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

13711

\[ {} x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right ) \]

13712

\[ {} x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t} \]

13839

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

13841

\[ {} x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]

13842

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

13853

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

13858

\[ {} y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x \]

13859

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

13862

\[ {} x^{\prime \prime \prime \prime }+x = t^{3} \]

13866

\[ {} y^{\left (6\right )}-y = {\mathrm e}^{2 x} \]

13867

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

13890

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

13900

\[ {} y^{\prime \prime \prime } = 1 \]

14010

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

14011

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