2.2.29 Problems 2801 to 2900

Table 2.75: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

2801

\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}

system_of_ODEs

0.405

2802

\begin{align*} x^{\prime }&=-7 x+y-6 z \\ y^{\prime }&=10 x-4 y+12 z \\ z^{\prime }&=2 x-y+z \\ \end{align*}

system_of_ODEs

0.881

2803

\begin{align*} x^{\prime }&=3 x+2 y+4 z \\ y^{\prime }&=2 x+2 z \\ z^{\prime }&=4 x+2 y+3 z \\ \end{align*}

system_of_ODEs

0.741

2804

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

system_of_ODEs

0.740

2805

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

system_of_ODEs

0.672

2806

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

system_of_ODEs

0.919

2807

\begin{align*} x^{\prime }&=2 y+z \\ y^{\prime }&=-2 x+h \\ z^{\prime }&=2 h \\ h^{\prime }&=-2 z \\ \end{align*}

system_of_ODEs

0.823

2808

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

[_quadrature]

2.581

2809

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

[_quadrature]

1.904

2810

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

[_quadrature]

4.379

2811

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

system_of_ODEs

0.037

2812

\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\ \end{align*}

system_of_ODEs

1.029

2813

\begin{align*} x^{\prime }&=x-x^{3}-x y \\ y^{\prime }&=2 y-y^{5}-y \,x^{4} \\ \end{align*}

system_of_ODEs

0.038

2814

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

system_of_ODEs

0.033

2815

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

system_of_ODEs

0.037

2816

\begin{align*} x^{\prime }&=6 x-6 x^{2}-2 x y \\ y^{\prime }&=4 y-4 y^{2}-2 x y \\ \end{align*}

system_of_ODEs

0.038

2817

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

system_of_ODEs

0.073

2818

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

system_of_ODEs

0.063

2819

\begin{align*} z^{\prime \prime }+z^{3}&=0 \\ \end{align*}

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

12.026

2820

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

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

58.867

2821

\begin{align*} z^{\prime \prime }+{\mathrm e}^{z^{2}}&=1 \\ \end{align*}

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

3.415

2822

\begin{align*} z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\ \end{align*}

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

8.037

2823

\begin{align*} z^{\prime \prime }+z-2 z^{3}&=0 \\ \end{align*}

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

4.550

2824

\begin{align*} x_{1}^{\prime }&=-5 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-5 x_{2} \\ \end{align*}

system_of_ODEs

0.473

2825

\begin{align*} x_{1}^{\prime }&=-x_{2} \\ x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\ \end{align*}

system_of_ODEs

0.591

2826

\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\ \end{align*}

system_of_ODEs

0.539

2827

\begin{align*} x_{1}^{\prime }&=-4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-6 x_{2} \\ \end{align*}

system_of_ODEs

0.431

2828

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\ \end{align*}

system_of_ODEs

0.789

2829

\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*}

system_of_ODEs

0.513

2830

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

system_of_ODEs

1.822

2831

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*}

system_of_ODEs

0.690

2832

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-2 x_{2} \\ \end{align*}

system_of_ODEs

0.572

2833

\begin{align*} x_{1}^{\prime }&=4 x_{2} \\ x_{2}^{\prime }&=-9 x_{1} \\ \end{align*}

system_of_ODEs

0.561

2834

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

[[_2nd_order, _missing_x]]

3.969

2835

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

[[_2nd_order, _missing_x]]

3.271

2836

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

[[_2nd_order, _missing_x]]

5.484

2837

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

[[_2nd_order, _missing_x]]

2.730

2838

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

[[_2nd_order, _missing_x]]

0.594

2839

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

[[_2nd_order, _missing_x]]

2.690

2840

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

[_separable]

4.233

2841

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

[_separable]

12.010

2842

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

[_separable]

5.185

2843

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

[_separable]

5.406

2844

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

[_separable]

4.549

2845

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

[_separable]

5.415

2846

\begin{align*} \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

9.023

2847

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

[_separable]

4.820

2848

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

[_separable]

4.656

2849

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

[_separable]

5.901

2850

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

[_separable]

19.087

2851

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

[_quadrature]

0.457

2852

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

[_separable]

9.224

2853

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.967

2854

\begin{align*} \sec \left (x \right ) \cos \left (y\right )^{2}&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}

[_separable]

11.497

2855

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

[_separable]

6.314

2856

\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

5.938

2857

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

[_separable]

6.138

2858

\begin{align*} \tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

13.599

2859

\begin{align*} y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1&=0 \\ \end{align*}

[_separable]

25.127

2860

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

[_separable]

4.557

2861

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

[_separable]

6.711

2862

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

[_separable]

5.378

2863

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

[_separable]

11.829

2864

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

[_quadrature]

1.277

2865

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

[_quadrature]

3.204

2866

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

[_separable]

8.187

2867

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

[_separable]

16.217

2868

\begin{align*} \left (x^{2}+x +1\right ) y^{\prime }&=y^{2}+2 y+5 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

10.667

2869

\begin{align*} \left (x^{2}-2 x -8\right ) y^{\prime }&=y^{2}+y-2 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

10.088

2870

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

[_linear]

4.994

2871

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

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

21.734

2872

\begin{align*} -y+y^{\prime } x&=\sqrt {y x} \\ \end{align*}

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

28.010

2873

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

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

31.016

2874

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

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

59.191

2875

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

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

11.785

2876

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

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

25.844

2877

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

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

18.986

2878

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

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

37.861

2879

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

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

30.916

2880

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

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

31.872

2881

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

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

76.669

2882

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

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

11.232

2883

\begin{align*} y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \\ \end{align*}

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

10.122

2884

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

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

30.746

2885

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

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

21.308

2886

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

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

29.043

2887

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

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

35.204

2888

\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\ y \left (6\right ) &= \pi \\ \end{align*}

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

27.023

2889

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

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

50.131

2890

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

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

106.919

2891

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

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

4.477

2892

\begin{align*} y^{\prime }&=\frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \\ \end{align*}

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

15.188

2893

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

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

31.118

2894

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

28.424

2895

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

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

54.162

2896

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

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

31.692

2897

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

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

9.381

2898

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

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

31.201

2899

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

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

13.451

2900

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

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

12.977