4.8.5 Problems 401 to 500

Table 4.803: Third and higher order ode

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

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

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

6610

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

6611

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

6612

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

6613

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

6614

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

6615

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

6616

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

6617

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

6618

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

6619

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

6620

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

6621

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

6622

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

6623

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

6624

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

6625

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

6626

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

6627

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

6628

\[ {} y^{\prime \prime \prime }-7 y^{\prime }+6 y = 0 \]

6629

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

6630

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

6631

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

6632

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

6633

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

6634

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

6635

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

6636

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

6637

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

6638

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

6639

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

6640

\[ {} -15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6641

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

6642

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

6643

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

6644

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

6645

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

6646

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

6647

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

6648

\[ {} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6649

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

6650

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

6651

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

6652

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

6653

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

6654

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

6655

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

6656

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

6657

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

6658

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

6659

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]

6660

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

6661

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 0 \]

6662

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

6663

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

6664

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

6665

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

6666

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

6667

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

6668

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

6669

\[ {} \operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6670

\[ {} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 x y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6671

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