2.3.70 Problems 6901 to 7000

Table 2.689: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6901

2551

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

0.520

6902

5954

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

0.520

6903

6437

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

0.520

6904

8560

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

0.520

6905

8849

\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.520

6906

16621

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

0.520

6907

19877

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

0.520

6908

21112

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

0.520

6909

21910

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

0.520

6910

24590

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

0.520

6911

25125

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\ \end{align*}

0.520

6912

25587

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

0.520

6913

148

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

0.521

6914

157

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

0.521

6915

1901

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

0.521

6916

2625

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

0.521

6917

8112

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

0.521

6918

8488

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

0.521

6919

9612

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

0.521

6920

10477

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

0.521

6921

10589

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}

0.521

6922

15261

\begin{align*} y^{\prime \prime }-3 y^{\prime }-7 y&=4 \\ \end{align*}

0.521

6923

20917

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

0.521

6924

23038

\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=3 \cos \left (2 t \right ) \\ \end{align*}

0.521

6925

24080

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

0.521

6926

1405

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

0.522

6927

1453

\begin{align*} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align*}

0.522

6928

2265

\begin{align*} y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\ y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 6 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}

0.522

6929

2422

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

0.522

6930

3241

\begin{align*} 5 y^{\prime }-3 x^{\prime }-5 y&=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x&=0 \\ \end{align*}

0.522

6931

6728

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

0.522

6932

10028

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

0.522

6933

10029

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

0.522

6934

10061

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

0.522

6935

15197

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

0.522

6936

15705

\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.522

6937

16080

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.522

6938

16706

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

0.522

6939

16741

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \\ \end{align*}

0.522

6940

16916

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

0.522

6941

23442

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

0.522

6942

24922

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

0.522

6943

25597

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

0.522

6944

25598

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

0.522

6945

349

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=\left (x^{2}+1\right ) \sin \left (3 x \right ) \\ \end{align*}

0.523

6946

470

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

0.523

6947

1094

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

0.523

6948

4514

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}
Using Laplace transform method.

0.523

6949

5387

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

0.523

6950

8005

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

0.523

6951

9806

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

0.523

6952

10338

\begin{align*} y^{\prime } t +y&=0 \\ y \left (1\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.523

6953

16211

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

0.523

6954

16854

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

0.523

6955

16901

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

0.523

6956

17438

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \\ \end{align*}

0.523

6957

19428

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

0.523

6958

19671

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

0.523

6959

22221

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

0.523

6960

23830

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

0.523

6961

25272

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

0.523

6962

25599

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

0.523

6963

127

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

0.524

6964

338

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

0.524

6965

882

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

0.524

6966

1343

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\ \end{align*}

0.524

6967

3494

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

0.524

6968

4380

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

0.524

6969

6677

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

0.524

6970

8852

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

0.524

6971

15260

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

0.524

6972

17397

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

0.524

6973

19481

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

0.524

6974

19894

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}

0.524

6975

20102

\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}

0.524

6976

22175

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

0.524

6977

24020

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

0.524

6978

25124

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 t \,{\mathrm e}^{-3 t} \\ \end{align*}

0.524

6979

2241

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

0.525

6980

2243

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

0.525

6981

3404

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

0.525

6982

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*}

0.525

6983

8476

\begin{align*} \left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.525

6984

9713

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

0.525

6985

17377

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

0.525

6986

18697

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

0.525

6987

23074

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

0.525

6988

1894

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Series expansion around \(x=0\).

0.526

6989

2016

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.526

6990

2785

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

0.526

6991

3172

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

0.526

6992

7140

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

0.526

6993

9062

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

0.526

6994

9843

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

0.526

6995

16631

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}

0.526

6996

16988

\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\ \end{align*}

0.526

6997

17396

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.526

6998

17447

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\ \end{align*}

0.526

6999

18319

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

0.526

7000

19163

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

0.526