2.3.132 Problems 13101 to 13200

Table 2.795: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13101

8354

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

0.800

13102

13941

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

0.800

13103

14314

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

0.800

13104

15838

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

0.800

13105

17723

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

0.800

13106

19452

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

0.800

13107

23763

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

0.800

13108

25228

\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+9 y&=0 \\ \end{align*}

0.800

13109

2487

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

0.801

13110

7124

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

0.801

13111

19404

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

0.801

13112

20023

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

0.801

13113

20364

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

0.801

13114

20586

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

0.801

13115

23687

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

0.801

13116

3359

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

0.802

13117

6810

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

0.802

13118

9875

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

0.802

13119

9894

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

0.802

13120

10145

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

0.802

13121

12435

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

0.802

13122

14775

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

0.802

13123

14989

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

0.802

13124

4776

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

0.803

13125

5711

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

0.803

13126

7123

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

0.803

13127

13774

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

0.803

13128

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*}

0.803

13129

15534

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

0.803

13130

19885

\begin{align*} y^{\prime }+z^{\prime }+6 y&=0 \\ z^{\prime }+5 y+z&=0 \\ \end{align*}

0.803

13131

20564

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

0.803

13132

16499

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

0.804

13133

22354

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

0.804

13134

2464

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

0.805

13135

3364

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

0.805

13136

4124

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

0.805

13137

4511

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

0.805

13138

9895

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

0.805

13139

10396

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

0.805

13140

10418

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

0.805

13141

16925

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

0.805

13142

18946

\begin{align*} 2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.805

13143

23618

\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*}

0.805

13144

2008

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

0.806

13145

3888

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=3 x_{3}-x_{4} \\ x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\ \end{align*}

0.806

13146

5537

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

0.806

13147

9398

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

0.806

13148

10365

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

0.806

13149

16097

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

0.806

13150

18445

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

0.806

13151

21243

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

0.806

13152

23749

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

0.806

13153

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 \(x=0\).

0.806

13154

24952

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

0.806

13155

3325

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

0.807

13156

8158

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

0.807

13157

13163

\(\left [\begin {array}{cccc} 4 & 0 & 0 & -3 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 6 & 0 & 0 & -5 \end {array}\right ]\)

N/A

N/A

N/A

0.807

13158

21767

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

0.807

13159

12902

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

0.808

13160

13883

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

0.808

13161

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 \(x=0\).

0.809

13162

8592

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

0.809

13163

9921

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

0.809

13164

12554

\begin{align*} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y&=0 \\ \end{align*}

0.809

13165

13105

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

0.809

13166

14670

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

0.809

13167

18790

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

0.809

13168

20827

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

0.809

13169

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*}

0.810

13170

9860

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

0.810

13171

10176

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

0.810

13172

13160

\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\)

N/A

N/A

N/A

0.810

13173

25518

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

0.810

13174

11385

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

0.811

13175

15661

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

0.811

13176

19191

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

0.811

13177

125

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

0.812

13178

1610

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

0.812

13179

3119

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

0.812

13180

5928

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

0.812

13181

6476

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

0.812

13182

7976

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

0.812

13183

9237

\begin{align*} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\ \end{align*}

0.812

13184

15725

\begin{align*} y^{\prime \prime }+9 y&=\delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.812

13185

16944

\begin{align*} x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.812

13186

22998

\begin{align*} v^{\prime }&=60 t -4 v \\ v \left (0\right ) &= 0 \\ \end{align*}

0.812

13187

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 \(x=0\).

0.813

13188

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*}

0.813

13189

6545

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

0.813

13190

9731

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

0.813

13191

21151

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

0.813

13192

22143

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

0.813

13193

23051

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

0.813

13194

23581

\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -{\frac {5}{18}} \\ x_{2} \left (0\right ) &= {\frac {47}{9}} \\ \end{align*}

0.813

13195

1993

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

0.814

13196

6004

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

0.814

13197

13022

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

0.814

13198

19044

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

0.814

13199

20908

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

0.814

13200

21117

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

0.814