2.2.240 Problems 23901 to 24000

Table 2.493: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

23901

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

[_rational]

0.655

23902

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

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

5.706

23903

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

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

5.607

23904

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

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

5.884

23905

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

[[_linear, ‘class A‘]]

1.420

23906

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

[[_linear, ‘class A‘]]

2.867

23907

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

[[_linear, ‘class A‘]]

1.539

23908

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

[_linear]

1.534

23909

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

[_linear]

3.023

23910

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

[_linear]

3.765

23911

\begin{align*} y^{\prime }-\tan \left (x \right ) y&=\sin \left (x \right ) \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}

[_linear]

3.248

23912

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

[_linear]

2.792

23913

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

[_linear]

4.335

23914

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

[_linear]

3.685

23915

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

[_Bernoulli]

3.678

23916

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

[_Bernoulli]

5.319

23917

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

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

12.353

23918

\begin{align*} y^{5} y^{\prime }+5 y^{6}&=1 \\ \end{align*}

[_quadrature]

0.497

23919

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

[_separable]

4.291

23920

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

[[_2nd_order, _missing_y]]

1.420

23921

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

[[_2nd_order, _quadrature]]

1.306

23922

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.433

23923

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

[[_2nd_order, _missing_y]]

1.352

23924

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.641

23925

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

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

2.510

23926

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

[[_2nd_order, _missing_y]]

1.492

23927

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

[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.399

23928

\begin{align*} 6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.258

23929

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

[[_2nd_order, _with_linear_symmetries]]

0.349

23930

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

[[_2nd_order, _missing_x]]

2.044

23931

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

[[_2nd_order, _missing_x]]

1.764

23932

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

system_of_ODEs

0.029

23933

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

system_of_ODEs

0.454

23934

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

system_of_ODEs

0.299

23935

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

system_of_ODEs

0.027

23936

\begin{align*} y^{\prime }+2 z&=y \\ z^{\prime }+4 y&=0 \\ \end{align*}

system_of_ODEs

0.524

23937

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

system_of_ODEs

0.586

23938

\begin{align*} y^{\prime }&=x^{2}+6 y+4 z \\ z^{\prime }&=y+3 z \\ \end{align*}

system_of_ODEs

0.616

23939

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

system_of_ODEs

0.424

23940

\begin{align*} y^{\prime }&=f \left (x \right )+a y+b z \\ z^{\prime }&=g \left (x \right )+c y+d z \\ \end{align*}

system_of_ODEs

3.954

23941

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

[_separable]

3.945

23942

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

[_exact]

4.099

23943

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

[[_high_order, _missing_x]]

0.043

23944

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

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

8.732

23945

\begin{align*} y^{\prime }&=\frac {1}{x^{5}+y x} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

6.366

23946

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

[_separable]

3.794

23947

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

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

6.636

23948

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

[_separable]

5.933

23949

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

[_exact]

5.257

23950

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

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

3.463

23951

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

system_of_ODEs

0.025

23952

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

[[_3rd_order, _missing_x]]

0.086

23953

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

[_exact, _rational]

4.209

23954

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.677

23955

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

[[_1st_order, _with_linear_symmetries], _rational]

3.023

23956

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

[_separable]

7.239

23957

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

[_separable]

3.297

23958

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

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

14.931

23959

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

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

5.915

23960

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

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

17.132

23961

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

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

5.749

23962

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

system_of_ODEs

2.244

23963

\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.288

23964

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

[[_2nd_order, _missing_y]]

0.467

23965

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

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

75.100

23966

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.674

23967

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.236

23968

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

[[_linear, ‘class A‘]]

3.010

23969

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

[[_linear, ‘class A‘]]

5.379

23970

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

[[_linear, ‘class A‘]]

4.293

23971

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

[_separable]

3.910

23972

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

[_linear]

2.976

23973

\begin{align*} y^{\prime \prime }-5 y^{\prime }-y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.212

23974

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

[[_2nd_order, _missing_x]]

0.236

23975

\begin{align*} y^{\prime \prime }-2 y^{\prime }-4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.208

23976

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

[[_2nd_order, _missing_x]]

2.055

23977

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

[[_2nd_order, _missing_x]]

1.752

23978

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

[[_2nd_order, _missing_x]]

0.352

23979

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

[[_2nd_order, _missing_x]]

0.366

23980

\begin{align*} y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.230

23981

\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=x^{3} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.303

23982

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

[[_2nd_order, _with_linear_symmetries]]

0.358

23983

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

[[_2nd_order, _with_linear_symmetries]]

0.513

23984

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

[[_2nd_order, _missing_x]]

1.614

23985

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

[[_2nd_order, _with_linear_symmetries]]

0.379

23986

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

[[_2nd_order, _with_linear_symmetries]]

1.352

23987

\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{x}+3 \,{\mathrm e}^{-3 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.379

23988

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=1+2 x +3 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.403

23989

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

[[_2nd_order, _with_linear_symmetries]]

0.451

23990

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

[[_high_order, _missing_x]]

0.044

23991

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

[[_high_order, _missing_x]]

0.081

23992

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

[[_3rd_order, _missing_x]]

0.088

23993

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

[[_2nd_order, _with_linear_symmetries]]

0.298

23994

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

[[_high_order, _missing_y]]

0.102

23995

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

[[_2nd_order, _with_linear_symmetries]]

0.389

23996

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

[[_high_order, _linear, _nonhomogeneous]]

0.153

23997

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

[[_high_order, _linear, _nonhomogeneous]]

0.110

23998

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

[[_3rd_order, _missing_y]]

0.098

23999

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.144

24000

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

[[_high_order, _linear, _nonhomogeneous]]

1.965