2.2.239 Problems 23801 to 23900

Table 2.491: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

23801

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

system_of_ODEs

0.245

23802

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

system_of_ODEs

0.246

23803

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

system_of_ODEs

0.246

23804

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

system_of_ODEs

0.285

23805

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

system_of_ODEs

0.200

23806

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

system_of_ODEs

0.198

23807

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

system_of_ODEs

0.232

23808

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

system_of_ODEs

0.235

23809

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

system_of_ODEs

0.326

23810

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

system_of_ODEs

0.282

23811

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

system_of_ODEs

0.303

23812

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

system_of_ODEs

0.276

23813

\begin{align*} x^{\prime }&=4 x+6 y \\ y^{\prime }&=-7 x-9 y \\ \end{align*}

system_of_ODEs

0.336

23814

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

system_of_ODEs

0.300

23815

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

system_of_ODEs

0.027

23816

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

system_of_ODEs

0.029

23817

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

system_of_ODEs

0.031

23818

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

system_of_ODEs

0.030

23819

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

system_of_ODEs

0.023

23820

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

system_of_ODEs

0.700

23821

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

system_of_ODEs

0.335

23822

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

system_of_ODEs

0.657

23823

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

system_of_ODEs

0.348

23824

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

system_of_ODEs

0.197

23825

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

system_of_ODEs

0.206

23826

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

system_of_ODEs

0.237

23827

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

system_of_ODEs

0.563

23828

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

[_quadrature]

0.280

23829

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

[_quadrature]

0.199

23830

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

[_quadrature]

0.172

23831

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

[_quadrature]

0.181

23832

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

[_quadrature]

0.206

23833

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

[_quadrature]

0.194

23834

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

[_quadrature]

0.205

23835

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

[[_Riccati, _special]]

43.588

23836

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

[[_linear, ‘class A‘]]

0.799

23837

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

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

4.799

23838

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

[_rational, _Riccati]

2.365

23839

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

[_quadrature]

0.199

23840

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

[[_linear, ‘class A‘]]

0.816

23841

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

[_separable]

0.166

23842

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

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

3.068

23843

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

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

4.313

23844

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

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

5.616

23845

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

[_linear]

2.137

23846

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.312

23847

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.954

23848

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

[[_2nd_order, _with_linear_symmetries]]

0.272

23849

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

[_separable]

2.374

23850

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

[_separable]

2.569

23851

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

[_separable]

2.809

23852

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

[_separable]

2.636

23853

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

[_separable]

5.404

23854

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

[_separable]

7.068

23855

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

[_separable]

2.124

23856

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

[_separable]

1.916

23857

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

[_separable]

2.526

23858

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

[_separable]

3.159

23859

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

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

3.133

23860

\begin{align*} 2 x^{3} y+\left (2 y^{2} x^{2}+2 y^{4}+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[‘x=_G(y,y’)‘]

1.648

23861

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

[_linear]

3.493

23862

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

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

6.275

23863

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

[‘y=_G(x,y’)‘]

11.457

23864

\begin{align*} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

15.720

23865

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

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

2.702

23866

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

[[_homogeneous, ‘class G‘], _rational]

3.720

23867

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

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

4.942

23868

\begin{align*} y^{\prime }&=\frac {y x +3}{5 x -y} \\ \end{align*}

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

11.670

23869

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

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

4.982

23870

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

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

4.825

23871

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

[_rational]

6.158

23872

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

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

6.386

23873

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

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

4.362

23874

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

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

9.015

23875

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

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

20.098

23876

\begin{align*} y^{\prime }&=1+\frac {3 y}{x} \\ \end{align*}

[_linear]

4.222

23877

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

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

23.133

23878

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

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

10.627

23879

\begin{align*} y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \\ \end{align*}

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

7.420

23880

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

[_exact, _rational]

2.566

23881

\begin{align*} 3 y^{2} x^{2}-4 y+\left (3 y^{2}-4 x +2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational]

2.788

23882

\begin{align*} 3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

3.837

23883

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

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

5.716

23884

\begin{align*} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational]

3.123

23885

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

[_exact]

14.068

23886

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

3.565

23887

\begin{align*} \frac {1-6 x^{2} y}{x}+\frac {\left (2+5 y-3 x^{2} y\right ) y^{\prime }}{y}&=0 \\ \end{align*}

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

24.409

23888

\begin{align*} \frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}

[_rational]

59.580

23889

\begin{align*} \frac {y^{5} x^{2}+y^{2}+y}{1+x^{2} y^{4}}+\frac {\left (y^{4} x^{3}+2 y x +x \right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}

[_exact, _rational]

3.101

23890

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

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

2.971

23891

\begin{align*} 2 x^{2} y-y^{2}+6 x^{3} y^{3}+\left (2 x^{4} y^{2}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

3.450

23892

\begin{align*} x^{4}-3 y+3 y^{\prime }&=0 \\ \end{align*}

[[_linear, ‘class A‘]]

4.007

23893

\begin{align*} 20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

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

18.464

23894

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

[_rational, _Bernoulli]

1.946

23895

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

[_linear]

4.138

23896

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

[_linear]

3.424

23897

\begin{align*} y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

3.685

23898

\begin{align*} 2 x y^{2}+2 x +\left (6 y^{3}+2 y+4 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

3.389

23899

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

4.078

23900

\begin{align*} 2 x +2 x y^{2}-y^{3}-y^{5}+\left (1-3 x y^{2}-3 y^{4} x \right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

3.182