2.3.102 Problems 10101 to 10200

Table 2.753: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10101

8798

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

0.768

10102

10137

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

0.768

10103

12392

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

0.768

10104

18200

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

0.768

10105

20537

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

0.768

10106

3242

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

0.769

10107

7113

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

0.769

10108

15306

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

0.769

10109

18891

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=t \cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.769

10110

26126

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

0.769

10111

8516

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

0.770

10112

9748

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

0.770

10113

17497

\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}

0.770

10114

20930

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

0.770

10115

23572

\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*}

0.770

10116

23743

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

0.770

10117

24576

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

0.770

10118

3177

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

0.771

10119

3373

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

0.771

10120

3845

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

0.771

10121

3869

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

0.771

10122

8597

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.771

10123

9478

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

0.771

10124

9709

\begin{align*} x^{\prime }&=5 x+9 y+2 \\ y^{\prime }&=-x+11 y+6 \\ \end{align*}

0.771

10125

10249

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

0.771

10126

18918

\begin{align*} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}

0.771

10127

23617

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

0.771

10128

2006

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

0.772

10129

7186

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

0.772

10130

7949

\begin{align*} 16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}

0.772

10131

8605

\begin{align*} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.772

10132

9598

\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=10 x^{3}-2 x +5 \\ \end{align*}
Series expansion around \(x=0\).

0.772

10133

15274

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

0.772

10134

20532

\begin{align*} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\ \end{align*}

0.772

10135

3139

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

0.773

10136

3495

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

0.773

10137

3585

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

0.773

10138

6204

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

0.773

10139

6213

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

0.773

10140

7292

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \\ \end{align*}

0.773

10141

8598

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

0.773

10142

14776

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

0.773

10143

14783

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

0.773

10144

15287

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

0.773

10145

17510

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{2}+1} \\ \end{align*}

0.773

10146

18151

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\ \end{align*}

0.773

10147

21588

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}

0.773

10148

21722

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.773

10149

23628

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}

0.773

10150

23719

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

0.773

10151

24626

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4-8 x +6 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.773

10152

7105

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

0.774

10153

8820

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

0.774

10154

8942

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

0.774

10155

9741

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

0.774

10156

14069

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

0.774

10157

15299

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

0.774

10158

19650

\begin{align*} x^{\prime }&=x+y-5 t +2 \\ y^{\prime }&=4 x-2 y-8 t -8 \\ \end{align*}

0.774

10159

22615

\begin{align*} s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\ \end{align*}

0.774

10160

23732

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{16}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.774

10161

1750

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

0.775

10162

3324

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

0.775

10163

3748

\begin{align*} y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\ \end{align*}

0.775

10164

5485

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

0.775

10165

8803

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

0.775

10166

11714

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

0.775

10167

22696

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

0.775

10168

23616

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

0.775

10169

3161

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

0.776

10170

7280

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\ \end{align*}

0.776

10171

10015

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

0.776

10172

16726

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\ \end{align*}

0.776

10173

16839

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

0.776

10174

18373

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

0.776

10175

21149

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

0.776

10176

25218

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

0.776

10177

25464

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

0.776

10178

1386

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

0.777

10179

8523

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

0.777

10180

8580

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

0.777

10181

8946

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

0.777

10182

12924

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )&=0 \\ \end{align*}

0.777

10183

13895

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

0.777

10184

19643

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

0.777

10185

21315

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

0.777

10186

23726

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

0.777

10187

24738

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

0.777

10188

26114

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

0.777

10189

2283

\begin{align*} y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\ y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\ \end{align*}

0.778

10190

6175

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

0.778

10191

7101

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

0.778

10192

7287

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

0.778

10193

7346

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=6 \,{\mathrm e}^{2 x} \\ \end{align*}

0.778

10194

7578

\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\ \end{align*}

0.778

10195

19012

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

0.778

10196

21247

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

0.778

10197

23085

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 x} \sin \left (3 x \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -{\frac {25}{6}} \\ \end{align*}

0.778

10198

2589

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

0.779

10199

4087

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

0.779

10200

6161

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

0.779