2.3.130 Problems 12901 to 13000

Table 2.833: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12901

18994

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 11 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

1.148

12902

2003

\begin{align*} x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.149

12903

3901

\begin{align*} x_{1}^{\prime }&=-4 x_{1} \\ x_{2}^{\prime }&=2 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=5 x_{2}-x_{3} \\ \end{align*}

1.149

12904

8618

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

Series expansion around \(x=0\).

1.149

12905

12595

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

1.149

12906

14943

\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \\ \end{align*}

1.149

12907

5676

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

1.150

12908

12871

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

1.150

12909

5980

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

1.151

12910

6153

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

1.151

12911

7620

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

1.151

12912

12847

\begin{align*} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}}&=0 \\ \end{align*}

1.151

12913

16180

\begin{align*} x y^{\prime \prime }+2&=\sqrt {x} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}

1.151

12914

2010

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

Series expansion around \(x=0\).

1.152

12915

2292

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

1.152

12916

8864

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

1.152

12917

15635

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

1.152

12918

16438

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

1.152

12919

18864

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

1.152

12920

2464

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

Series expansion around \(t=0\).

1.153

12921

14209

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

1.153

12922

14638

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

1.153

12923

21738

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

1.153

12924

221

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

1.154

12925

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 \(x=0\).

1.154

12926

12418

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

1.154

12927

16178

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

1.154

12928

17098

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

1.154

12929

2008

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

Series expansion around \(x=0\).

1.155

12930

4482

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

1.155

12931

15636

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

1.155

12932

15439

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

1.156

12933

23374

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

1.156

12934

23629

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ u \left (0\right ) &= 0 \\ \end{align*}

1.156

12935

24535

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

1.156

12936

1832

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

1.157

12937

3400

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

Series expansion around \(x=0\).

1.157

12938

10275

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

1.157

12939

14974

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

Series expansion around \(x=0\).

1.157

12940

19264

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

1.157

12941

26368

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

1.157

12942

5785

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

1.158

12943

9410

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

Series expansion around \(x=-1\).

1.158

12944

11821

\begin{align*} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\ \end{align*}

1.158

12945

19143

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

1.158

12946

20772

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

1.158

12947

20994

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

1.158

12948

24582

\begin{align*} y^{\prime \prime }-y^{\prime }&=42 \,{\mathrm e}^{4 x} \\ \end{align*}

1.158

12949

24873

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

1.158

12950

3866

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

1.159

12951

7181

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

Series expansion around \(x=0\).

1.159

12952

14061

\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1&=0 \\ \end{align*}

1.159

12953

19848

\begin{align*} e y^{\prime \prime }&=\frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \\ \end{align*}

1.159

12954

21755

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

1.159

12955

23918

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

1.159

12956

25335

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

Series expansion around \(t=0\).

1.159

12957

8588

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

Series expansion around \(x=0\).

1.160

12958

15164

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

1.160

12959

16048

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

1.161

12960

19150

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

1.161

12961

20635

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

1.161

12962

22759

\begin{align*} y^{\prime \prime }&=\frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

1.161

12963

24847

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

1.161

12964

25585

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

1.161

12965

1519

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

1.162

12966

22215

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

Series expansion around \(x=0\).

1.162

12967

22916

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

1.162

12968

11712

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

1.163

12969

14138

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

1.163

12970

3280

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

1.164

12971

6104

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

1.164

12972

8096

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

Series expansion around \(x=0\).

1.164

12973

15759

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

1.164

12974

18825

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

1.164

12975

24691

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

1.164

12976

18990

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+6 x_{3} \\ x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }&=6 x_{1}+x_{2}+x_{3} \\ \end{align*}

1.165

12977

19664

\begin{align*} x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\ x \left (1\right ) &= 0 \\ \end{align*}

1.165

12978

4019

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

Series expansion around \(x=0\).

1.166

12979

15072

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

1.166

12980

21741

\begin{align*} x^{\prime }&=7 x-y+6 z \\ y^{\prime }&=-10 x+4 y-12 z \\ z^{\prime }&=-2 x+y-z \\ \end{align*}

1.166

12981

1825

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

1.167

12982

1828

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

1.167

12983

5729

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

1.167

12984

8089

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

Series expansion around \(x=0\).

1.167

12985

11384

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

1.167

12986

12587

\begin{align*} y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )} \\ \end{align*}

1.167

12987

18157

\begin{align*} y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \\ \end{align*}

1.167

12988

18333

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

1.167

12989

22176

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

Series expansion around \(x=0\).

1.167

12990

2394

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

1.168

12991

4044

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

Series expansion around \(x=0\).

1.168

12992

9668

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

1.168

12993

9739

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

1.168

12994

12681

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

1.168

12995

20143

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

1.168

12996

25306

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

Using Laplace transform method.

1.168

12997

2005

\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.169

12998

4140

\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.169

12999

9750

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

1.169

13000

16925

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

Series expansion around \(x=1\).

1.169