6.66 Problems 6501 to 6600

Table 6.131: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

6501

\[ {} y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

6502

\[ {} x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

6503

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

6504

\[ {} \frac {x^{\prime \prime }}{2} = -48 x \]

6505

\[ {} x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]

6506

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

6507

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

6508

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

6509

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

6510

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

6511

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

6512

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

6513

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

6514

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

6515

\[ {} y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \]

6516

\[ {} y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

6517

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

6518

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

6519

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

6520

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

6521

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

6522

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

6523

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

6524

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

6525

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

6526

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x} \]

6527

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

6528

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

6529

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

6530

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

6531

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

6532

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

6533

\[ {} y^{\prime }+\frac {4 y}{x} = x^{4} \]

6534

\[ {} y^{\prime \prime \prime \prime } = 5 x \]

6535

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

6536

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

6537

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

6538

\[ {} y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

6539

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

6540

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

6541

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

6542

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

6543

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

6544

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

6545

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

6546

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

6547

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

6548

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

6549

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

6550

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

6551

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

6552

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

6553

\[ {} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \]

6554

\[ {} y^{\prime \prime \prime }-y = 5 \]

6555

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

6556

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

6557

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

6558

\[ {} q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]

6559

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

6560

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

6561

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

6562

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

6563

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

6564

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

6565

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

6566

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

6567

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

6568

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

6569

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

6570

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

6571

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

6572

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

6573

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

6574

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

6575

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

6576

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

6577

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

6578

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

6579

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

6580

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

6581

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

6582

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

6583

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

6584

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

6585

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

6586

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

6587

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

6588

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

6589

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

6590

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

6591

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

6592

\[ {} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

6593

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

6594

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

6595

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

6596

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

6597

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

6598

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

6599

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

6600

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