2.3.112 Problems 11101 to 11200

Table 2.797: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11101

21613

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

0.704

11102

21675

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

Series expansion around \(x=0\).

0.704

11103

22776

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

0.704

11104

22782

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

0.704

11105

22836

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

Series expansion around \(x=1\).

0.704

11106

2762

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

With initial conditions

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

0.705

11107

10064

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

0.705

11108

10525

\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 y x^{5}&=0 \\ \end{align*}

0.705

11109

14647

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=27 \,{\mathrm e}^{-6 x} \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.705

11110

16746

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.705

11111

18643

\begin{align*} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }&=\frac {x}{2}+y-\frac {23}{2} \\ \end{align*}

0.705

11112

21330

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

0.705

11113

23988

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

0.705

11114

14682

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

0.706

11115

14790

\begin{align*} x^{\prime }&=5 x+2 y+5 t \\ y^{\prime }&=3 x+4 y+17 t \\ \end{align*}

0.706

11116

16080

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.706

11117

25571

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

0.706

11118

27066

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

Series expansion around \(x=0\).

0.706

11119

5807

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

0.707

11120

6293

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

0.707

11121

6717

\begin{align*} 2 y x +2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=10 x^{2}+10 \\ \end{align*}

0.707

11122

8093

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

Series expansion around \(x=0\).

0.707

11123

8352

\begin{align*} s^{\prime }&=k s \\ \end{align*}

0.707

11124

11319

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

0.707

11125

15161

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

0.707

11126

15276

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

0.707

11127

19652

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

0.707

11128

20140

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

0.707

11129

20206

\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}

0.707

11130

20598

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

0.707

11131

22704

\begin{align*} i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \\ i \left (0\right ) &= 4 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.707

11132

23535

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

0.707

11133

23690

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

Series expansion around \(x=-2\).

0.707

11134

23822

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

0.707

11135

23995

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

0.707

11136

24582

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

0.707

11137

3767

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

0.708

11138

14317

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

0.708

11139

16658

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \\ \end{align*}

0.708

11140

19772

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

0.708

11141

24071

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

0.708

11142

27691

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

0.708

11143

1845

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

Series expansion around \(x=2\).

0.709

11144

3766

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

0.709

11145

10585

\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*}

0.709

11146

19191

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

0.709

11147

1030

\begin{align*} x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\ \end{align*}

0.710

11148

1826

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

0.710

11149

2464

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

Series expansion around \(t=0\).

0.710

11150

4542

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

0.710

11151

6220

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

0.710

11152

6380

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

0.710

11153

7081

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \\ \end{align*}

0.710

11154

7667

\begin{align*} x^{\prime \prime }+42 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.710

11155

7673

\begin{align*} y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.710

11156

14686

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

0.710

11157

14689

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

0.710

11158

16352

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

0.710

11159

16387

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

0.710

11160

16589

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.710

11161

17483

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\ \end{align*}

0.710

11162

18257

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

0.710

11163

19606

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

Series expansion around \(x=0\).

0.710

11164

19780

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

0.710

11165

23556

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

With initial conditions

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

0.710

11166

23691

\begin{align*} \left (-x^{2}+4 x -3\right ) y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+6 y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}

Series expansion around \(x=2\).

0.710

11167

24052

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

Using Laplace transform method.

0.710

11168

27064

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

Series expansion around \(x=0\).

0.710

11169

619

\begin{align*} x_{1}^{\prime }&=-8 x_{1}-11 x_{2}-2 x_{3} \\ x_{2}^{\prime }&=6 x_{1}+9 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-6 x_{1}-6 x_{2}+x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -7 \\ x_{3} \left (0\right ) &= 11 \\ \end{align*}

0.711

11170

6405

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

0.711

11171

8863

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

0.711

11172

13207

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

0.711

11173

18016

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

0.711

11174

20448

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

0.711

11175

20916

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

Using Laplace transform method.

0.711

11176

21754

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

0.711

11177

22213

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

Series expansion around \(x=0\).

0.711

11178

26950

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

0.711

11179

2278

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

0.712

11180

9562

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

0.712

11181

9575

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

0.712

11182

17696

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

Series expansion around \(x=0\).

0.712

11183

20447

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

0.712

11184

2708

\begin{align*} x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\ y^{\prime }&=-x+f_{2} \left (t \right ) \\ \end{align*}

With initial conditions

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

0.713

11185

9567

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

0.713

11186

9901

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

Series expansion around \(x=0\).

0.713

11187

10944

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

0.713

11188

12981

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

0.713

11189

16743

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \\ \end{align*}

0.713

11190

20663

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

0.713

11191

23462

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=x^{2} {\mathrm e}^{5 x} \\ \end{align*}

0.713

11192

26600

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

0.713

11193

26971

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=9 \cos \left (3 x \right ) \\ \end{align*}

0.713

11194

985

\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

0.714

11195

1996

\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.714

11196

2080

\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.714

11197

5774

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=8 x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.714

11198

6855

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

0.714

11199

7300

\begin{align*} y^{\prime \prime }+y&=8 x \sin \left (x \right ) \\ \end{align*}

0.714

11200

7840

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

Series expansion around \(x=0\).

0.714