4.20.23 Problems 2201 to 2300

Table 4.1243: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

14470

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

14471

\[ {} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \]

14472

\[ {} x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]

14473

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

14475

\[ {} x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]

14478

\[ {} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \]

14479

\[ {} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right ) \]

14480

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

14482

\[ {} x^{\prime \prime }-x = \delta \left (t -5\right ) \]

14483

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

14484

\[ {} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]

14485

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

14486

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

14487

\[ {} x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]

14528

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = 0 \]

14529

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

14535

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

14536

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

14537

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

14540

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

14542

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

14545

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

14546

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

14547

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

14548

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

14670

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \]

14671

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \]

14673

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]

14674

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

14677

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

14678

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

14686

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

14687

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 2-12 x +6 \,{\mathrm e}^{x} \]

14688

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

14689

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

14690

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \]

14691

\[ {} 3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \]

14692

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

14693

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

14694

\[ {} y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

14695

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

14696

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

14697

\[ {} y^{\prime \prime }+6 y^{\prime }+25 y = 0 \]

14698

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

14699

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

14700

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 0 \]

14701

\[ {} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y = 0 \]

14702

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

14703

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

14704

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

14705

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \]

14706

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

14707

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

14708

\[ {} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y = 0 \]

14709

\[ {} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y = 0 \]

14710

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

14711

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

14712

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

14713

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

14714

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

14715

\[ {} 3 y^{\prime \prime }+4 y^{\prime }-4 y = 0 \]

14716

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

14717

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

14718

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

14719

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

14720

\[ {} y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]

14721

\[ {} y^{\prime \prime }+6 y^{\prime }+58 y = 0 \]

14722

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

14723

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

14724

\[ {} 9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \]

14725

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

14726

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]

14727

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \]

14728

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0 \]

14729

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

14730

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

14731

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y = 0 \]

14732

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

14733

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

14734

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

14735

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

14736

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

14737

\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 16 x -12 \,{\mathrm e}^{2 x} \]

14738

\[ {} y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \]

14739

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x} \]

14740

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

14741

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

14742

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

14743

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

14744

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \]

14745

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

14746

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

14747

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

14748

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

14749

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

14750

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

14751

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

14752

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

14753

\[ {} y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \]

14754

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