2.2.159 Problems 15801 to 15900

Table 2.335: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

15801

\begin{align*} y^{\prime }&=2 y+1 \\ y \left (0\right ) &= 3 \\ \end{align*}

[_quadrature]

1.257

15802

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

[_separable]

4.961

15803

\begin{align*} x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\ x \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.406

15804

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

[_quadrature]

2.644

15805

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

[_separable]

4.114

15806

\begin{align*} y^{\prime }&=\frac {1}{2 y+3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

0.900

15807

\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

3.595

15808

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

[_quadrature]

1.463

15809

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

[_quadrature]

0.337

15810

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

[_quadrature]

0.321

15811

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

[_quadrature]

0.798

15812

\begin{align*} y^{\prime }&=4 y^{2} \\ \end{align*}

[_quadrature]

2.530

15813

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

[_quadrature]

1.833

15814

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

[[_linear, ‘class A‘]]

1.431

15815

\begin{align*} y^{\prime }&=3 y \left (1-y\right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_quadrature]

2.601

15816

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

[[_linear, ‘class A‘]]

2.625

15817

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

[_Riccati]

4.024

15818

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

[_separable]

5.591

15819

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_quadrature]

13.928

15820

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_quadrature]

13.687

15821

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

18.240

15822

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}

[_quadrature]

67.544

15823

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}

[_quadrature]

20.520

15824

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

[_quadrature]

2.127

15825

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

[_quadrature]

1.444

15826

\begin{align*} y^{\prime }&=y^{3}+y^{2} \\ \end{align*}

[_quadrature]

18.918

15827

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

[_quadrature]

0.404

15828

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

[_separable]

7.889

15829

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

[_separable]

4.130

15830

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

[_separable]

3.716

15831

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

[_quadrature]

0.407

15832

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \end{align*}

[_quadrature]

22.206

15833

\begin{align*} \theta ^{\prime }&=2 \\ \end{align*}

[_quadrature]

1.056

15834

\begin{align*} \theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\ \end{align*}

[_quadrature]

22.142

15835

\begin{align*} v^{\prime }&=-\frac {v}{R C} \\ \end{align*}

[_quadrature]

2.396

15836

\begin{align*} v^{\prime }&=\frac {K -v}{R C} \\ \end{align*}

[_quadrature]

0.724

15837

\begin{align*} v^{\prime }&=2 V \left (t \right )-2 v \\ \end{align*}

[[_linear, ‘class A‘]]

2.752

15838

\begin{align*} y^{\prime }&=2 y+1 \\ y \left (0\right ) &= 3 \\ \end{align*}

[_quadrature]

1.633

15839

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

[[_Riccati, _special]]

8.389

15840

\begin{align*} y^{\prime }&=y^{2}-4 t \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[[_Riccati, _special]]

9.105

15841

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

[_quadrature]

10.028

15842

\begin{align*} w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\ w \left (0\right ) &= 4 \\ \end{align*}

[_quadrature]

1.993

15843

\begin{align*} w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\ w \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

1.839

15844

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

[_quadrature]

1.787

15845

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

[_quadrature]

1.717

15846

\begin{align*} y^{\prime }&=y^{2}-y^{3} \\ y \left (0\right ) &= {\frac {1}{5}} \\ \end{align*}

[_quadrature]

21.290

15847

\begin{align*} y^{\prime }&=2 y^{3}+t^{2} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}

[_Abel]

3.229

15848

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

[_quadrature]

4.569

15849

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

[_quadrature]

1.788

15850

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \theta \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

28.075

15851

\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}

[_quadrature]

6.482

15852

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

[_quadrature]

8.255

15853

\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

8.497

15854

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

[_quadrature]

4.249

15855

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

[_quadrature]

3.658

15856

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

[_quadrature]

16.454

15857

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

[_separable]

8.536

15858

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

[_quadrature]

0.928

15859

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

[_separable]

7.916

15860

\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

2.711

15861

\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (-2\right ) &= -1 \\ \end{align*}

[_quadrature]

4.005

15862

\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}

[_quadrature]

2.730

15863

\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

8.349

15864

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

3.379

15865

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

2.171

15866

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 6 \\ \end{align*}

[_quadrature]

5.240

15867

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 5 \\ \end{align*}

[_quadrature]

2.043

15868

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

[_quadrature]

5.508

15869

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

[_quadrature]

24.747

15870

\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (0\right ) &= -\frac {\pi }{2} \\ \end{align*}

[_quadrature]

8.998

15871

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

[_quadrature]

3.495

15872

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

[_quadrature]

4.568

15873

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

[_quadrature]

3.842

15874

\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (3\right ) &= 1 \\ \end{align*}

[_quadrature]

4.638

15875

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

[_quadrature]

4.076

15876

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

[_quadrature]

4.645

15877

\begin{align*} w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\ \end{align*}

[_quadrature]

8.352

15878

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

[_quadrature]

2.036

15879

\begin{align*} v^{\prime }&=-v^{2}-2 v-2 \\ \end{align*}

[_quadrature]

0.758

15880

\begin{align*} w^{\prime }&=3 w^{3}-12 w^{2} \\ \end{align*}

[_quadrature]

16.022

15881

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

[_quadrature]

1.917

15882

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

[_quadrature]

3.040

15883

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

[_quadrature]

28.061

15884

\begin{align*} w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\ \end{align*}

[_quadrature]

6.359

15885

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= -1 \\ \end{align*}

[_quadrature]

1.215

15886

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

0.836

15887

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_quadrature]

1.104

15888

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= -4 \\ \end{align*}

[_quadrature]

0.924

15889

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_quadrature]

1.140

15890

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (3\right ) &= 1 \\ \end{align*}

[_quadrature]

1.871

15891

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

[_quadrature]

2.727

15892

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

[_quadrature]

2.535

15893

\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}

[_quadrature]

2.690

15894

\begin{align*} y^{\prime }&=y^{3}-y^{2} \\ \end{align*}

[_quadrature]

11.393

15895

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

[_quadrature]

7.743

15896

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

[_quadrature]

1.850

15897

\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}

[_quadrature]

2.236

15898

\begin{align*} y^{\prime }&=y^{2}-y^{3} \\ \end{align*}

[_quadrature]

12.869

15899

\begin{align*} y^{\prime }&=-4 y+9 \,{\mathrm e}^{-t} \\ \end{align*}

[[_linear, ‘class A‘]]

2.474

15900

\begin{align*} y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\ \end{align*}

[[_linear, ‘class A‘]]

2.079