4.3.51 Problems 5001 to 5100

Table 4.465: Second order ode

#

ODE

Mathematica

Maple

Sympy

14444

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

14445

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

14446

\[ {} x^{\prime \prime }-x = \frac {1}{t} \]

14447

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

14448

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

14449

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

14450

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]

14451

\[ {} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

14452

\[ {} x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \]

14453

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

14454

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

14455

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

14456

\[ {} x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}} = 0 \]

14457

\[ {} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0 \]

14467

\[ {} x^{\prime \prime }-x^{\prime }-6 x = 0 \]

14468

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

14469

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

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

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

14530

\[ {} 2 y+4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0 \]

14535

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

14540

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

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

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

14672

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

14673

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

14674

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

14675

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

14676

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

14677

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

14680

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

14681

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

14682

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

14683

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

14684

\[ {} \left (2 x +1\right ) y^{\prime \prime }-4 y^{\prime } \left (1+x \right )+4 y = 0 \]

14685

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

14686

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

14687

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

14688

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

14689

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

14690

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

14691

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

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

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

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

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

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

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

14744

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

14745

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

14752

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

14753

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

14756

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

14757

\[ {} y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]

14758

\[ {} y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x} \]

14759

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \]

14760

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

14761

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]

14762

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]