2.3.122 Problems 12101 to 12200

Table 2.775: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12101

12615

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

0.683

12102

13073

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

0.683

12103

16913

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

0.683

12104

18368

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

0.683

12105

19131

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

0.683

12106

20907

\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 \(x=0\).

0.683

12107

1385

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

0.684

12108

4544

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

0.684

12109

7374

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

0.684

12110

8599

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

0.684

12111

10106

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

0.684

12112

17795

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

0.684

12113

18839

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

0.684

12114

20774

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

0.684

12115

21601

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

0.684

12116

23735

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

0.684

12117

3130

\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=5 \cos \left (6 x \right ) \\ \end{align*}

0.685

12118

3402

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

0.685

12119

7196

\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.685

12120

9268

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

0.685

12121

9751

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

0.685

12122

9809

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

0.685

12123

14125

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

0.685

12124

21520

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

0.685

12125

22094

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=0 \\ \end{align*}

0.685

12126

22274

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

0.685

12127

22475

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

0.685

12128

2078

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

0.686

12129

2263

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

0.686

12130

3889

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

0.686

12131

7355

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

0.686

12132

21651

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

0.686

12133

6640

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

0.687

12134

8066

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

0.687

12135

8522

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

0.687

12136

16268

\begin{align*} y^{\prime }&=4 y+16 x \\ \end{align*}

0.687

12137

16383

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

0.687

12138

18440

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

0.687

12139

20875

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

0.687

12140

21227

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

0.687

12141

21856

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

0.687

12142

22711

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

0.687

12143

315

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

0.688

12144

1345

\begin{align*} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\ \end{align*}

0.688

12145

5458

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

0.688

12146

5848

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

0.688

12147

9439

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

0.688

12148

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 \(x=0\).

0.688

12149

15290

\begin{align*} x^{\prime }&=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\ y^{\prime }&=-5 x+2 y+6 \,{\mathrm e}^{2 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.688

12150

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*}

0.688

12151

19577

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

0.688

12152

21304

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

0.688

12153

1950

\begin{align*} 8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.689

12154

6068

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

0.689

12155

9551

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

0.689

12156

10308

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

0.689

12157

13676

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

0.689

12158

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*}

0.689

12159

16653

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\cos \left (2 x \right ) x^{2} \\ \end{align*}

0.689

12160

17818

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.689

12161

19586

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

0.689

12162

19755

\begin{align*} v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\ \end{align*}

0.689

12163

20714

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

0.689

12164

23553

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

0.689

12165

24153

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

0.689

12166

25615

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

0.689

12167

1283

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

0.690

12168

6297

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

0.690

12169

7193

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

0.690

12170

9678

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

0.690

12171

10129

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

0.690

12172

20086

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

0.690

12173

25556

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

0.690

12174

25623

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

0.690

12175

1434

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align*}

0.691

12176

1964

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.691

12177

2182

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }&=-{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3 x +3\right ) \sin \left (3 x \right )\right ) \\ \end{align*}

0.691

12178

2603

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

0.691

12179

3267

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

0.691

12180

3376

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

0.691

12181

4009

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

0.691

12182

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*}

0.691

12183

6069

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

0.691

12184

7141

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

0.691

12185

8063

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

0.691

12186

9537

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

0.691

12187

9540

\begin{align*} y^{\prime \prime } x +y^{\prime }+10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.691

12188

12582

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

0.691

12189

14725

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

0.691

12190

16710

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

0.691

12191

18205

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

0.691

12192

20848

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=5+10 \sin \left (2 x \right ) \\ \end{align*}

0.691

12193

21523

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

0.691

12194

21531

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 x -40 \cos \left (2 x \right ) \\ \end{align*}

0.691

12195

23372

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

0.691

12196

1433

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

0.692

12197

3276

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

0.692

12198

7138

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

0.692

12199

8363

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

0.692

12200

10371

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

0.692