2.2.29 Problems 2801 to 2900

Table 2.71: 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

0.330

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

0.773

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

0.583

2804

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

system_of_ODEs

0.599

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

0.546

2806

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

system_of_ODEs

0.766

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

0.697

2808

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

[_quadrature]

1.017

2809

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

[_quadrature]

0.743

2810

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

[_quadrature]

1.431

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

0.030

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

0.928

2813

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

system_of_ODEs

0.050

2814

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

system_of_ODEs

0.038

2815

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

system_of_ODEs

0.033

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

0.037

2817

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

system_of_ODEs

0.046

2818

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

system_of_ODEs

0.050

2819

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

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

3.783

2820

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

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

49.891

2821

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

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

1.353

2822

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

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

2.559

2823

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

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

1.788

2824

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

system_of_ODEs

0.374

2825

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

system_of_ODEs

0.437

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

0.421

2827

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

system_of_ODEs

0.346

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

0.613

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

0.421

2830

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

system_of_ODEs

0.962

2831

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

system_of_ODEs

0.543

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

0.441

2833

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

system_of_ODEs

0.431

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]]

1.546

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]]

1.108

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]]

2.056

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]]

0.945

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]]

0.354

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]]

0.967

2840

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

[_separable]

2.011

2841

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

[_separable]

4.849

2842

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

[_separable]

2.830

2843

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

[_separable]

2.301

2844

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

[_separable]

1.996

2845

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

[_separable]

2.517

2846

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

[_separable]

3.828

2847

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

[_separable]

2.194

2848

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

[_separable]

2.240

2849

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

[_separable]

2.472

2850

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

[_separable]

4.572

2851

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

[_quadrature]

0.289

2852

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

[_separable]

3.483

2853

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

[_separable]

3.972

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]

8.708

2855

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

[_separable]

2.563

2856

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

[_separable]

2.494

2857

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

[_separable]

2.254

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]

8.823

2859

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

[_separable]

8.181

2860

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

[_separable]

2.248

2861

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

[_separable]

4.928

2862

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

[_separable]

3.149

2863

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

[_separable]

4.070

2864

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

[_quadrature]

0.730

2865

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

[_quadrature]

1.378

2866

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

[_separable]

3.991

2867

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

[_separable]

12.391

2868

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

[_separable]

7.496

2869

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

[_separable]

5.473

2870

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

[_linear]

2.333

2871

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

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

4.582

2872

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

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

9.710

2873

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

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

5.675

2874

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

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

23.800

2875

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

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

4.482

2876

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

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

7.059

2877

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

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

5.523

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‘]]

11.190

2879

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

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

5.546

2880

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

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

5.273

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]

58.076

2882

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

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

4.547

2883

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

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

5.877

2884

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

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

6.456

2885

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

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

6.342

2886

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

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

12.150

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‘]]

11.019

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]

6.251

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‘]]

11.307

2890

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

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

66.776

2891

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

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

1.974

2892

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

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

9.340

2893

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

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

14.944

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]

12.234

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‘]]

12.754

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‘]]

15.109

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‘]]

1.270

2898

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

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

14.857

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‘]]

6.072

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‘]]

5.682