2.3.70 Problems 6901 to 7000

Table 2.671: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6901

3319

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

0.594

6902

4685

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

0.594

6903

5663

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

0.594

6904

8501

\begin{align*} \left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.594

6905

9370

\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.594

6906

11095

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

0.594

6907

12911

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

0.594

6908

18632

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

0.594

6909

21243

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

0.594

6910

22209

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

0.594

6911

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*}

0.595

6912

3861

\begin{align*} x_{1}^{\prime }&=4 x_{1} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ x_{3}^{\prime }&=x_{2}+4 x_{3} \\ \end{align*}

0.595

6913

3872

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{2}+{\mathrm e}^{3 t} \\ \end{align*}

0.595

6914

8514

\begin{align*} 2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.595

6915

10221

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.595

6916

10812

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

0.595

6917

11127

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

0.595

6918

12981

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

0.595

6919

14987

\begin{align*} x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\ y^{\prime }&=x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.595

6920

15688

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \\ \end{align*}

0.595

6921

16836

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

0.595

6922

23625

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

0.595

6923

25340

\begin{align*} t^{2} y^{\prime \prime }+2 y^{\prime } t +t^{2} y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.595

6924

3998

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

0.596

6925

8131

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

0.596

6926

8516

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

0.596

6927

2007

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.597

6928

6516

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

0.597

6929

15244

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.597

6930

23604

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

0.597

6931

24811

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

0.597

6932

348

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

0.598

6933

485

\begin{align*} 4 y^{\prime \prime } x +8 y^{\prime }+y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.598

6934

487

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

0.598

6935

2783

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.598

6936

4036

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

0.598

6937

5676

\begin{align*} 3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\ \end{align*}

0.598

6938

6443

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

0.598

6939

11738

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

0.598

6940

14215

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

0.598

6941

16935

\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=3 x-y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -21 \\ \end{align*}

0.598

6942

17701

\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.598

6943

18454

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

0.598

6944

4188

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

0.599

6945

5662

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

0.599

6946

6405

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

0.599

6947

6501

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

0.599

6948

7961

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

0.599

6949

11085

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

0.599

6950

11134

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

0.599

6951

16849

\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y&=0 \\ \end{align*}
Series expansion around \(x=\frac {\pi }{2}\).

0.599

6952

16941

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

0.599

6953

19601

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

0.599

6954

21694

\begin{align*} 3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.599

6955

23752

\begin{align*} \left (x^{2}-\frac {1}{4}\right ) y^{\prime \prime }+2 y^{\prime }-6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.599

6956

23820

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

0.599

6957

25434

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

0.599

6958

1191

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

0.600

6959

2755

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.600

6960

10252

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.600

6961

11118

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

0.600

6962

19605

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

0.600

6963

493

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.601

6964

2006

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

0.601

6965

8594

\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.601

6966

9507

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

0.601

6967

10532

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}

0.601

6968

11265

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

0.601

6969

22275

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (1\right ) &= 0 \\ x_{2} \left (1\right ) &= 0 \\ \end{align*}

0.601

6970

23603

\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=17 x-7 y \\ \end{align*}

0.601

6971

1413

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }&=-\frac {x_{3}}{4} \\ \end{align*}

0.602

6972

2199

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 \cos \left (x \right ) x +2 \left (x +1\right ) \sin \left (x \right ) \\ \end{align*}

0.602

6973

7170

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

0.602

6974

8479

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.602

6975

9593

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

0.602

6976

11081

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

0.602

6977

11132

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}

0.602

6978

11145

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

0.602

6979

16706

\begin{align*} y^{\prime \prime \prime \prime }-81 y&=\sinh \left (x \right ) \\ \end{align*}

0.602

6980

11089

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

0.603

6981

14176

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

0.603

6982

21658

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

0.603

6983

2450

\begin{align*} 4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.604

6984

4017

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.604

6985

4228

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

0.604

6986

6883

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

0.604

6987

7641

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

0.604

6988

8123

\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.604

6989

20939

\begin{align*} x^{\prime }&=4 x-13 y \\ y^{\prime }&=2 x-6 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.604

6990

21893

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

0.604

6991

593

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

0.605

6992

6455

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

0.605

6993

6463

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

0.605

6994

11146

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

0.605

6995

15526

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

0.605

6996

17605

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

0.605

6997

20941

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

0.605

6998

21951

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

0.605

6999

1911

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

0.606

7000

2455

\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.606