2.2.80 Problems 7901 to 8000

Table 2.173: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

7901

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

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

0.189

7902

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

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

0.660

7903

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

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

0.194

7904

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

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

1.349

7905

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

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

0.252

7906

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

[_rational]

0.289

7907

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

[_linear]

0.152

7908

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

[_separable]

3.914

7909

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

[_linear]

0.142

7910

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

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

0.613

7911

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

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

0.677

7912

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

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

0.204

7913

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

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

0.180

7914

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

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

0.667

7915

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

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

0.284

7916

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

[_separable]

0.110

7917

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

[[_linear, ‘class A‘]]

1.530

7918

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

[_separable]

2.694

7919

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

[_linear]

3.539

7920

\begin{align*} i^{\prime }-6 i&=10 \sin \left (2 t \right ) \\ \end{align*}

[[_linear, ‘class A‘]]

1.907

7921

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.694

7922

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

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

3.108

7923

\begin{align*} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\ \end{align*}

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

7.099

7924

\begin{align*} y^{\prime } x +y-x^{3} y^{6}&=0 \\ \end{align*}

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

5.390

7925

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

[_linear]

2.263

7926

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

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

2.561

7927

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

[_separable]

3.474

7928

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

[‘y=_G(x,y’)‘]

4.347

7929

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

[_Bernoulli]

7.924

7930

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

[_linear]

14.019

7931

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

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

12.672

7932

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

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

6.915

7933

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

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

5.606

7934

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

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

4.317

7935

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

[_linear]

2.908

7936

\begin{align*} L i^{\prime }+R i&=E \sin \left (2 t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

2.480

7937

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

[‘y=_G(x,y’)‘]

2.920

7938

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

[_rational]

13.694

7939

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

[_Bernoulli]

3.090

7940

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

[_Abel]

3.737

7941

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

[‘y=_G(x,y’)‘]

2.589

7942

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

[_separable]

0.135

7943

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

[_quadrature]

0.182

7944

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

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

0.960

7945

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

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

0.756

7946

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

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

0.682

7947

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

[[_1st_order, _with_linear_symmetries], _rational]

0.754

7948

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.263

7949

\begin{align*} 16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational]

0.717

7950

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

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

0.339

7951

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

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

1.456

7952

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

[[_1st_order, _with_linear_symmetries]]

0.589

7953

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.991

7954

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

1.260

7955

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

[_quadrature]

9.721

7956

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

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

1.237

7957

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.282

7958

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

[[_1st_order, _with_linear_symmetries], _rational]

0.669

7959

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

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

0.931

7960

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

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

1.078

7961

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

[_quadrature]

0.417

7962

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

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

0.759

7963

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.467

7964

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

[_quadrature]

1.049

7965

\begin{align*} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.477

7966

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

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

69.691

7967

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

[[_2nd_order, _missing_x]]

0.194

7968

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.061

7969

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

[[_2nd_order, _with_linear_symmetries]]

0.305

7970

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (x \right ) x \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.559

7971

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

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

1.014

7972

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

[[_3rd_order, _with_linear_symmetries]]

0.287

7973

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

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

1.767

7974

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

7.589

7975

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

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

2.705

7976

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.812

7977

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.186

7978

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

[[_3rd_order, _missing_x]]

0.053

7979

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.257

7980

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.069

7981

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.271

7982

\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.103

7983

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.065

7984

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

[[_high_order, _missing_x]]

0.060

7985

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.069

7986

\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.092

7987

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.287

7988

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

[[_2nd_order, _missing_x]]

1.179

7989

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

[[_3rd_order, _missing_x]]

0.110

7990

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

[[_high_order, _missing_x]]

0.141

7991

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

[[_3rd_order, _missing_y]]

0.119

7992

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.381

7993

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

[[_2nd_order, _with_linear_symmetries]]

0.318

7994

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.392

7995

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.413

7996

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.532

7997

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.351

7998

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.478

7999

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.352

8000

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.553