2.3.102 Problems 10101 to 10200

Table 2.777: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10101

26738

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

With initial conditions

\begin{align*} x \left (0\right ) &= {\frac {119}{900}} \\ y \left (0\right ) &= {\frac {211}{900}} \\ \end{align*}

0.756

10102

637

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

0.757

10103

654

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

0.757

10104

3505

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

Series expansion around \(z=0\).

0.757

10105

5317

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

0.757

10106

8079

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

Series expansion around \(x=0\).

0.757

10107

8136

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

Series expansion around \(x=0\).

0.757

10108

9848

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

Series expansion around \(x=0\).

0.757

10109

10173

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

Series expansion around \(x=0\).

0.757

10110

15428

\begin{align*} s^{\prime \prime }-a^{2} s&=t +1 \\ \end{align*}

0.757

10111

15572

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

0.757

10112

18266

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\left (12 x -7\right ) {\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.757

10113

18460

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

Using Laplace transform method.

0.757

10114

21651

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

Series expansion around \(x=0\).

0.757

10115

22501

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

0.757

10116

27663

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

0.757

10117

27702

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

0.757

10118

1990

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

Series expansion around \(x=0\).

0.758

10119

2261

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

0.758

10120

9602

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

Using Laplace transform method.

0.758

10121

22165

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

0.758

10122

26448

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

0.758

10123

27174

\begin{align*} x_{1}^{\prime }&=3 x_{1}+3 x_{2}+8 \\ x_{2}^{\prime }&=x_{1}+5 x_{2}+4 \,{\mathrm e}^{3 t} \\ \end{align*}

0.758

10124

27706

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

0.758

10125

3838

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=5 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=2 x_{2}-4 x_{3} \\ \end{align*}

0.759

10126

10263

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

0.759

10127

15073

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

0.759

10128

15263

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

0.759

10129

15464

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

0.759

10130

18193

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

0.759

10131

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*}

0.759

10132

20348

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

0.759

10133

24560

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

0.759

10134

487

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

Series expansion around \(x=0\).

0.760

10135

898

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

0.760

10136

2828

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

0.760

10137

4499

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

0.760

10138

7817

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

0.760

10139

8810

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

0.760

10140

10240

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}

0.760

10141

14281

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

0.760

10142

14794

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

With initial conditions

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

0.760

10143

14926

\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.760

10144

15732

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= -2 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}

0.760

10145

16816

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\delta \left (-4+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.760

10146

18902

\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

0.760

10147

19011

\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*}

0.760

10148

19971

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

0.760

10149

20944

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

0.760

10150

21272

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

Series expansion around \(t=0\).

0.760

10151

21301

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

0.760

10152

21893

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

0.760

10153

22140

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

0.760

10154

26976

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

0.760

10155

8052

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

0.761

10156

12869

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

0.761

10157

14109

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

0.761

10158

19699

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

0.761

10159

22152

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

0.761

10160

22798

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

0.761

10161

22824

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

Series expansion around \(x=0\).

0.761

10162

24755

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

0.761

10163

2280

\begin{align*} y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\ \end{align*}

0.762

10164

7173

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

Series expansion around \(x=0\).

0.762

10165

14285

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

0.762

10166

14964

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

0.762

10167

15248

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}

Using Laplace transform method.

0.762

10168

15608

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

0.762

10169

18411

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

0.762

10170

22662

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

0.762

10171

348

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

0.763

10172

512

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.763

10173

2001

\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.763

10174

8853

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

0.763

10175

8939

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

0.763

10176

10175

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

Series expansion around \(x=0\).

0.763

10177

18226

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

0.763

10178

21218

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

0.763

10179

22142

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

0.763

10180

22837

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

Series expansion around \(x=0\).

0.763

10181

25195

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.763

10182

25245

\begin{align*} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\ \end{align*}

Using Laplace transform method.

0.763

10183

6591

\begin{align*} h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

0.764

10184

12605

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

0.764

10185

17517

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

0.764

10186

18384

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

Series expansion around \(x=0\).

0.764

10187

19610

\begin{align*} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.764

10188

22190

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

Series expansion around \(x=0\).

0.764

10189

22729

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

0.764

10190

2752

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

0.765

10191

3253

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

0.765

10192

10455

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

Series expansion around \(x=0\).

0.765

10193

15772

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

0.765

10194

17896

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

0.765

10195

18398

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

0.765

10196

27584

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

0.765

10197

2461

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

Series expansion around \(t=0\).

0.766

10198

3768

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

0.766

10199

6696

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

0.766

10200

8413

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (0\right ) &= -1 \\ \end{align*}

0.766