6.86 Problems 8501 to 8600

Table 6.171: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

8501

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

8502

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

8503

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

8504

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

8505

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

8506

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

8507

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

8508

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

8509

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

8510

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

8511

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

8512

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

8513

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

8514

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

8515

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

8516

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

8517

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

8518

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

8519

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

8520

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

8521

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

8522

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

8523

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

8524

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

8525

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

8526

\[ {}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

8527

\[ {}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \]

8528

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

8529

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

8530

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

8531

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

8532

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

8533

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

8534

\[ {}6 x {y^{\prime }}^{2}-\left (2 y+3 x \right ) y^{\prime }+y = 0 \]

8535

\[ {}9 {y^{\prime }}^{2}+3 y^{4} y^{\prime } x +y^{5} = 0 \]

8536

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

8537

\[ {}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0 \]

8538

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

8539

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

8540

\[ {}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0 \]

8541

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

8542

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

8543

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

8544

\[ {}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0 \]

8545

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

8546

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

8547

\[ {}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0 \]

8548

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

8549

\[ {}x^{6} {y^{\prime }}^{2} = 16 y+8 x y^{\prime } \]

8550

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

8551

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

8552

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

8553

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

8554

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

8555

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

8556

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

8557

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

8558

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

8559

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

8560

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

8561

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

8562

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

8563

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y = 0 \]

8564

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

8565

\[ {}\left (x^{2}-9\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \]

8566

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

8567

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

8568

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+3 y = 0 \]

8569

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

8570

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

8571

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

8572

\[ {}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

8573

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

8574

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

8575

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

8576

\[ {}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0 \]

8577

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

8578

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

8579

\[ {}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0 \]

8580

\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0 \]

8581

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y = 0 \]

8582

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

8583

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

8584

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

8585

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

8586

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

8587

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

8588

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

8589

\[ {}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0 \]

8590

\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \]

8591

\[ {}8 x^{2} y^{\prime \prime }+10 x y^{\prime }-\left (1+x \right ) y = 0 \]

8592

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

8593

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

8594

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

8595

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

8596

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

8597

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

8598

\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0 \]

8599

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

8600

\[ {}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0 \]