2.3.91 Problems 9001 to 9100

Table 2.713: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9001

11064

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

0.924

9002

15862

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

0.924

9003

19151

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

0.924

9004

25397

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

0.924

9005

38

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

0.925

9006

220

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.925

9007

3507

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

0.925

9008

3867

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

0.925

9009

4061

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

0.925

9010

6428

\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+{y^{\prime }}^{2} \\ \end{align*}

0.925

9011

9668

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

0.925

9012

13012

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

0.925

9013

16668

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \\ \end{align*}

0.925

9014

8911

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

0.926

9015

9406

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

0.926

9016

17787

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

0.926

9017

4541

\begin{align*} x^{\prime }-x-2 y&={\mathrm e}^{t} \\ -4 x+y^{\prime }-3 y&=1 \\ \end{align*}

0.927

9018

23228

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

0.927

9019

25804

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

0.927

9020

3057

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

0.928

9021

18992

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align*}

0.928

9022

22981

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

0.928

9023

24099

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

0.928

9024

25419

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

0.928

9025

23288

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

0.929

9026

6508

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

0.930

9027

9529

\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 \(x=0\).

0.930

9028

9552

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

0.930

9029

12852

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

0.930

9030

16881

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

0.930

9031

17832

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

0.930

9032

19140

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

0.931

9033

19887

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

0.931

9034

23206

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

0.931

9035

3348

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

0.932

9036

11091

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

0.932

9037

12861

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

0.932

9038

19040

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

0.932

9039

2764

\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*}

0.933

9040

6893

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

0.933

9041

10479

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

0.933

9042

11086

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

0.933

9043

23750

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

0.933

9044

7308

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

0.934

9045

10750

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

0.934

9046

10863

\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}

0.934

9047

22104

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

0.934

9048

24549

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

0.934

9049

25281

\begin{align*} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \\ \end{align*}
Using Laplace transform method.

0.934

9050

5215

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

0.935

9051

9725

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

0.935

9052

19056

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }&=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }&=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \\ \end{align*}

0.935

9053

3351

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

0.936

9054

8865

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

0.936

9055

10472

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

0.936

9056

10539

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

0.936

9057

20903

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

0.936

9058

5574

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

0.937

9059

9542

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

0.938

9060

15288

\begin{align*} x^{\prime }&=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }&=9 x-3 y+12 \cos \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.938

9061

6406

\begin{align*} -6+x y \left (12+3 y x -2 y^{2} x^{2}\right )+x^{2} \left (9+2 y x \right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \\ \end{align*}

0.939

9062

15443

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

0.939

9063

20452

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

0.939

9064

23011

\begin{align*} 38 x^{\prime \prime }+10 x^{\prime }-3 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.939

9065

3395

\begin{align*} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\ \end{align*}
Series expansion around \(x=0\).

0.940

9066

5557

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

0.940

9067

6334

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

0.940

9068

11272

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

0.940

9069

12908

\begin{align*} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 y x \right ) y^{\prime }+b +x y \left (a +3 y x -2 y^{2} x^{2}\right )&=0 \\ \end{align*}

0.940

9070

151

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

0.941

9071

1946

\begin{align*} x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.941

9072

2730

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3} \\ \end{align*}

0.941

9073

5362

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

0.941

9074

9533

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

0.941

9075

4032

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

0.942

9076

9408

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

0.942

9077

14427

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

0.942

9078

15756

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

0.943

9079

2759

\begin{align*} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.944

9080

5400

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

0.944

9081

9813

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

0.944

9082

12290

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

0.944

9083

13488

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

0.944

9084

16908

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

0.944

9085

21702

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

0.944

9086

23339

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

0.944

9087

23918

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

0.944

9088

25292

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.944

9089

18645

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

0.945

9090

19000

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

0.945

9091

20505

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\ \end{align*}

0.945

9092

8255

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

0.946

9093

9556

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

0.946

9094

9991

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

0.946

9095

19119

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

0.946

9096

23680

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

0.946

9097

838

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

0.947

9098

1261

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

0.947

9099

7151

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

0.947

9100

16411

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

0.947