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]

29.193

25502

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

[_separable]

27.490

25503

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

[_separable]

53.456

25504

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

[_separable]

35.494

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]

517.423

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’)‘]

37.712

25507

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

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

147.808

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]

487.855

25509

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

[_separable]

0.508

25510

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

[_linear]

3.799

25511

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

[[_2nd_order, _missing_x]]

5.237

25512

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

[[_2nd_order, _missing_y]]

0.726

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]]

1.869

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]]

4.457

25515

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

[[_2nd_order, _missing_x]]

29.690

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]]

90.970

25517

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

[[_2nd_order, _missing_x]]

12.839

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]]

17.530

25519

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.220

25520

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

[[_high_order, _missing_x]]

0.203

25521

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

[[_2nd_order, _with_linear_symmetries]]

1.925

25522

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

[[_2nd_order, _with_linear_symmetries]]

2.140

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]]

8.839

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]]

2.792

25525

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.089

25526

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

[[_2nd_order, _linear, _nonhomogeneous]]

12.306

25527

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

[[_2nd_order, _linear, _nonhomogeneous]]

8.879

25528

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

[[_2nd_order, _missing_x]]

119.973

25529

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

[[_2nd_order, _quadrature]]

5.138

25530

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

[[_2nd_order, _quadrature]]

3.217

25531

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

[[_2nd_order, _with_linear_symmetries]]

7.093

25532

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

[_quadrature]

15.546

25533

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

[[_2nd_order, _missing_x]]

26.205

25534

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

[[_2nd_order, _missing_x]]

11.168

25535

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

[[_2nd_order, _missing_x]]

0.886

25536

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

[[_high_order, _missing_x]]

0.451

25537

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

[[_2nd_order, _missing_x]]

0.955

25538

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

[[_high_order, _missing_x]]

0.467

25539

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

[[_2nd_order, _missing_x]]

4.654

25540

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

[[_2nd_order, _missing_x]]

1.016

25541

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

[[_2nd_order, _missing_x]]

1.096

25542

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

[[_high_order, _missing_x]]

0.325

25543

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

[[_2nd_order, _quadrature]]

5.876

25544

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

[[_2nd_order, _quadrature]]

9.026

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]]

15.326

25546

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.235

25547

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

[[_2nd_order, _with_linear_symmetries]]

1.810

25548

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

[[_2nd_order, _with_linear_symmetries]]

1.493

25549

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

[[_2nd_order, _with_linear_symmetries]]

1.604

25550

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

[[_2nd_order, _with_linear_symmetries]]

2.037

25551

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

[[_high_order, _with_linear_symmetries]]

10.164

25552

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

[[_2nd_order, _with_linear_symmetries]]

1.269

25553

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

[[_3rd_order, _with_linear_symmetries]]

0.843

25554

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

[[_2nd_order, _with_linear_symmetries]]

5.075

25555

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

[[_2nd_order, _with_linear_symmetries]]

3.624

25556

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

[[_2nd_order, _missing_x]]

22.164

25557

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

[[_2nd_order, _with_linear_symmetries]]

4.111

25558

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

[[_2nd_order, _missing_x]]

11.339

25559

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

[[_2nd_order, _with_linear_symmetries]]

10.121

25560

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

[[_2nd_order, _missing_x]]

9.377

25561

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

[[_2nd_order, _missing_x]]

15.358

25562

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

[[_2nd_order, _with_linear_symmetries]]

10.066

25563

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

[[_2nd_order, _missing_x]]

8.767

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]]

8.074

25565

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

[[_2nd_order, _missing_x]]

7.984

25566

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.642

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]]

2.756

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]]

2.489

25569

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

[[_2nd_order, _with_linear_symmetries]]

2.698

25570

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

[[_2nd_order, _with_linear_symmetries]]

1.598

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]]

6.442

25572

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

[[_2nd_order, _linear, _nonhomogeneous]]

8.900

25573

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

[[_2nd_order, _linear, _nonhomogeneous]]

22.079

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]]

19.997

25575

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.474

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]]

9.203

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]]

9.967

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]]

2.911

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]]

3.539

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]]

3.729

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]]

16.678

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]]

12.388

25583

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

[[_2nd_order, _missing_x]]

12.476

25584

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

[[_2nd_order, _missing_x]]

8.500

25585

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

[[_2nd_order, _quadrature]]

3.718

25586

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

[[_2nd_order, _with_linear_symmetries]]

1.896

25587

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

[[_2nd_order, _with_linear_symmetries]]

1.914

25588

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.171

25589

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.827

25590

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

[[_2nd_order, _with_linear_symmetries]]

1.875

25591

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

[[_2nd_order, _with_linear_symmetries]]

1.907

25592

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.918

25593

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

[[_2nd_order, _missing_y]]

4.205

25594

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

[[_2nd_order, _missing_y]]

4.471

25595

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.359

25596

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.349

25597

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

[[_2nd_order, _with_linear_symmetries]]

1.887

25598

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.893

25599

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.908

25600

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.835