2.2.256 Problems 25501 to 25600

Table 2.529: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

25501

\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}

[_separable]

4.098

25502

\begin{align*} y^{\prime }&=-4 t y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.968

25503

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

15.882

25504

\begin{align*} \left (1+t \right ) y^{\prime }&=4 y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.822

25505

\begin{align*} y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

22.368

25506

\begin{align*} y^{\prime }&=-\frac {1+{\mathrm e}^{t y} y}{2 y+{\mathrm e}^{t y} t} \\ \end{align*}

[‘x=_G(y,y’)‘]

22.945

25507

\begin{align*} y^{\prime }&=\frac {4 t -y}{t -6 y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

23.801

25508

\begin{align*} y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18.512

25509

\begin{align*} y^{\prime }&=-\frac {y}{2 t} \\ \end{align*}

[_separable]

0.182

25510

\begin{align*} y^{\prime }&=a t y+q \\ y \left (0\right ) &= 0 \\ \end{align*}

[_linear]

0.353

25511

\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.556

25512

\begin{align*} 2 t y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.183

25513

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.429

25514

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.397

25515

\begin{align*} m y^{\prime \prime }+k y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.457

25516

\begin{align*} m y^{\prime \prime }+k \sin \left (y\right )&=0 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

47.020

25517

\begin{align*} y^{\prime \prime }&=-9 y \\ \end{align*}

[[_2nd_order, _missing_x]]

2.809

25518

\begin{align*} y^{\prime \prime }&=-9 y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.240

25519

\begin{align*} y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.588

25520

\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}

[[_high_order, _missing_x]]

0.055

25521

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.441

25522

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.533

25523

\begin{align*} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.302

25524

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.580

25525

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.589

25526

\begin{align*} m y^{\prime \prime }+k y&=\delta \left (-t +T \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.635

25527

\begin{align*} m y^{\prime \prime }+k y&=f \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.330

25528

\begin{align*} m y^{\prime \prime }+k y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

68.132

25529

\begin{align*} y^{\prime \prime }&=f \left (t \right ) \\ \end{align*}

[[_2nd_order, _quadrature]]

0.996

25530

\begin{align*} y^{\prime \prime }&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _quadrature]]

0.866

25531

\begin{align*} m y^{\prime \prime }-k y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.145

25532

\begin{align*} y^{\prime }&=a y \\ \end{align*}

[_quadrature]

1.821

25533

\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.505

25534

\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+\omega ^{2}\right ) y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.169

25535

\begin{align*} 2 y^{\prime \prime }+8 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.217

25536

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.078

25537

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.300

25538

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.086

25539

\begin{align*} 4 y^{\prime \prime }+B y^{\prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.656

25540

\begin{align*} y^{\prime \prime }&=2 a y^{\prime }-\left (a^{2}-\omega ^{2}\right ) y \\ \end{align*}

[[_2nd_order, _missing_x]]

0.266

25541

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.333

25542

\begin{align*} y^{\left (8\right )}&=y \\ \end{align*}

[[_high_order, _missing_x]]

0.094

25543

\begin{align*} y^{\prime \prime }&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _quadrature]]

1.056

25544

\begin{align*} y^{\prime \prime }&=\operatorname {Direct}_{t} \\ \end{align*}

[[_2nd_order, _quadrature]]

1.608

25545

\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.781

25546

\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.409

25547

\begin{align*} y^{\prime \prime }+3 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.503

25548

\begin{align*} 2 y^{\prime \prime }+4 y&={\mathrm e}^{i t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.547

25549

\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{-3 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.396

25550

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.500

25551

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

1.667

25552

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{t} {\mathrm e}^{i t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.446

25553

\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{i t} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.347

25554

\begin{align*} y^{\prime \prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.836

25555

\begin{align*} y^{\prime \prime }+5 y^{\prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.751

25556

\begin{align*} y^{\prime \prime }+k y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.439

25557

\begin{align*} y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.735

25558

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.196

25559

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.152

25560

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.982

25561

\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.942

25562

\begin{align*} y^{\prime \prime }+\omega _{n}^{2} y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.539

25563

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.968

25564

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.995

25565

\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=f \\ \end{align*}

[[_2nd_order, _missing_x]]

1.045

25566

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=5 \cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.417

25567

\begin{align*} y^{\prime \prime }+y&=\sin \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.552

25568

\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.544

25569

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.453

25570

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.462

25571

\begin{align*} y^{\prime \prime }+2 z y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.661

25572

\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\sqrt {\frac {k}{m}}\, t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.428

25573

\begin{align*} a y^{\prime \prime }+b y^{\prime }+c y&=f \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

2.656

25574

\begin{align*} 4 a y^{\prime \prime }+b y^{\prime }+\frac {c y}{4}&=f \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

2.428

25575

\begin{align*} g^{\prime \prime }-3 g^{\prime }+2 g&=\delta \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.518

25576

\begin{align*} y^{\prime \prime }+b y^{\prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.854

25577

\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.012

25578

\begin{align*} r^{\prime \prime }+\frac {5 r^{\prime }}{2}+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.466

25579

\begin{align*} r^{\prime \prime }+2 r^{\prime }+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.549

25580

\begin{align*} r^{\prime \prime }+r^{\prime }+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.595

25581

\begin{align*} r^{\prime \prime }+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.789

25582

\begin{align*} y^{\prime \prime }+2 p y^{\prime }+\omega _{n}^{2} y&=\omega _{n}^{2} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.327

25583

\begin{align*} y^{\prime \prime }+y&=4 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.881

25584

\begin{align*} y^{\prime \prime }+y^{\prime }&=4 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.226

25585

\begin{align*} y^{\prime \prime }&=4 \\ \end{align*}

[[_2nd_order, _quadrature]]

0.771

25586

\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.440

25587

\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.457

25588

\begin{align*} y^{\prime \prime }-y&=\cos \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.453

25589

\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.505

25590

\begin{align*} y^{\prime \prime }+y&=t +{\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.448

25591

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.438

25592

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.469

25593

\begin{align*} y^{\prime \prime }+y^{\prime }&=1+t \\ \end{align*}

[[_2nd_order, _missing_y]]

0.933

25594

\begin{align*} y^{\prime \prime }+y^{\prime }&=t^{2}+1 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.943

25595

\begin{align*} y^{\prime \prime }+3 y&=\cos \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.567

25596

\begin{align*} y^{\prime \prime }+3 y&=t \cos \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.739

25597

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.461

25598

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{3} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.469

25599

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\cos \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.469

25600

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t \sin \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.636