4.20.12 Problems 1101 to 1200

Table 4.1221: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

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

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

4470

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 36 x \,{\mathrm e}^{2 x} \]

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

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

4474

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

4475

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

4476

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

4477

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

4478

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

4479

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \left (1+x \right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \]

4480

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

4481

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

4482

\[ {} -y+y^{\prime \prime } = 12 x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \]

4483

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

4484

\[ {} y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (x^{2}+10\right ) \]

4485

\[ {} y^{\prime \prime }-4 y = 96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \]

4486

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

4487

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

4488

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

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

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

4497

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

4498

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

4499

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

4500

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

4501

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

4502

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

4503

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

4504

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

4505

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 15 \,{\mathrm e}^{-x} \sqrt {1+x} \]

4506

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

4507

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

4508

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

4514

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right ) \]

4515

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

4516

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1 \]

4517

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

4518

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

4519

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

4520

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

4521

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t} \]

4522

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \]

4523

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

4524

\[ {} y^{\prime \prime }+4 y = 8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \]

4525

\[ {} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \]

4526

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

4527

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right ) \]

4528

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

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

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

5715

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

5716

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

5717

\[ {} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \]

5718

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

5719

\[ {} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \]

5720

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

5721

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

5722

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

5723

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

5724

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

5725

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

5726

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

5727

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

5728

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

5729

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

5730

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

5731

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

5732

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

5733

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

5734

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

5735

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

5736

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

5737

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

5738

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

5739

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

5740

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

5741

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

5742

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

5743

\[ {} y^{\prime \prime }+a^{2} y = x^{2}+x +1 \]

5744

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

5745

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

5746

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

5773

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

5774

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

5775

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

5776

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

5777

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

5778

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

5779

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