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]

1.212

15802

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

[_separable]

3.564

15803

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

[_separable]

2.797

15804

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

[_quadrature]

2.156

15805

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

[_separable]

3.787

15806

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

[_quadrature]

0.830

15807

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

[_separable]

3.237

15808

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

[_quadrature]

1.117

15809

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

[_quadrature]

0.400

15810

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

[_quadrature]

0.368

15811

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

[_quadrature]

0.878

15812

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

[_quadrature]

2.078

15813

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

[_quadrature]

1.251

15814

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

[[_linear, ‘class A‘]]

1.251

15815

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

[_quadrature]

1.267

15816

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

[[_linear, ‘class A‘]]

1.539

15817

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

[_Riccati]

2.829

15818

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

[_separable]

2.912

15819

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

[_quadrature]

20.250

15820

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

[_quadrature]

19.204

15821

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

[_quadrature]

18.746

15822

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

[_quadrature]

59.471

15823

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

[_quadrature]

17.478

15824

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

[_quadrature]

1.192

15825

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

[_quadrature]

0.977

15826

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

[_quadrature]

9.285

15827

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

[_quadrature]

0.400

15828

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

[_separable]

3.806

15829

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

[_separable]

2.676

15830

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

[_separable]

2.461

15831

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

[_quadrature]

0.424

15832

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

[_quadrature]

23.875

15833

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

[_quadrature]

0.786

15834

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

[_quadrature]

23.684

15835

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

[_quadrature]

1.251

15836

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

[_quadrature]

0.544

15837

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

[[_linear, ‘class A‘]]

1.760

15838

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

[_quadrature]

1.178

15839

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

[[_Riccati, _special]]

4.154

15840

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

[[_Riccati, _special]]

4.061

15841

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

[_quadrature]

5.954

15842

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

[_quadrature]

1.092

15843

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

[_quadrature]

0.923

15844

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

[_quadrature]

1.193

15845

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

[_quadrature]

1.134

15846

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

[_quadrature]

12.944

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]

2.131

15849

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

[_quadrature]

1.052

15850

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

[_quadrature]

23.905

15851

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

[_quadrature]

3.286

15852

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

[_quadrature]

4.300

15853

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

[_quadrature]

3.593

15854

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

[_quadrature]

1.967

15855

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

[_quadrature]

2.038

15856

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

[_quadrature]

8.336

15857

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

[_separable]

5.416

15858

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

[_quadrature]

0.641

15859

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

[_separable]

4.322

15860

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

[_quadrature]

1.544

15861

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

[_quadrature]

2.698

15862

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

[_quadrature]

1.586

15863

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

[_quadrature]

4.853

15864

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

[_quadrature]

1.296

15865

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

[_quadrature]

1.279

15866

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

[_quadrature]

2.582

15867

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

[_quadrature]

1.229

15868

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

[_quadrature]

2.605

15869

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

[_quadrature]

25.070

15870

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

[_quadrature]

4.758

15871

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

[_quadrature]

3.017

15872

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

[_quadrature]

3.077

15873

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

[_quadrature]

2.931

15874

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

[_quadrature]

3.038

15875

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

[_quadrature]

3.006

15876

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

[_quadrature]

2.982

15877

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

[_quadrature]

5.545

15878

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

[_quadrature]

1.404

15879

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

[_quadrature]

0.615

15880

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

[_quadrature]

10.692

15881

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

[_quadrature]

1.385

15882

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

[_quadrature]

2.073

15883

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

[_quadrature]

12.327

15884

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

[_quadrature]

4.194

15885

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

[_quadrature]

1.044

15886

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

[_quadrature]

0.588

15887

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

[_quadrature]

0.865

15888

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

[_quadrature]

1.892

15889

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

[_quadrature]

0.877

15890

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

[_quadrature]

1.695

15891

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

[_quadrature]

2.260

15892

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

[_quadrature]

1.513

15893

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

[_quadrature]

2.275

15894

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

[_quadrature]

11.307

15895

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

[_quadrature]

5.023

15896

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

[_quadrature]

1.174

15897

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

[_quadrature]

1.969

15898

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

[_quadrature]

9.151

15899

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

[[_linear, ‘class A‘]]

1.844

15900

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

[[_linear, ‘class A‘]]

1.595