2.3.102 Problems 10101 to 10200

Table 2.735: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10101

15667

\begin{align*} y^{\prime \prime }+9 y&=27 x +18 \\ y \left (0\right ) &= 23 \\ y^{\prime }\left (0\right ) &= 21 \\ \end{align*}

0.523

10102

15993

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

0.523

10103

16092

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=-8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.523

10104

17463

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -{\frac {5}{16}} \\ y^{\prime }\left (0\right ) &= {\frac {9}{16}} \\ \end{align*}

0.523

10105

22357

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

0.523

10106

23562

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

0.523

10107

524

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

0.524

10108

2035

\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.524

10109

6514

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

0.524

10110

6565

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

0.524

10111

15277

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

0.524

10112

16121

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \cos \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.524

10113

16874

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

0.524

10114

17510

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

0.524

10115

17683

\begin{align*} y^{\prime \prime }+3 y^{\prime }-18 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.524

10116

18286

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

0.524

10117

18682

\begin{align*} x^{\prime }&=4 x+a y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.524

10118

18832

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

0.524

10119

19550

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 y^{\prime \prime } x -8 y^{\prime }&=0 \\ \end{align*}

0.524

10120

22797

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

0.524

10121

23535

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

0.524

10122

23554

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

0.524

10123

23936

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

0.524

10124

314

\begin{align*} a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \\ \end{align*}

0.525

10125

1940

\begin{align*} \left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (-x +2\right ) y&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= -2 \\ \end{align*}
Series expansion around \(x=3\).

0.525

10126

2179

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y&=8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \\ \end{align*}

0.525

10127

2639

\begin{align*} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.525

10128

5519

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

0.525

10129

5626

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

0.525

10130

6444

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

0.525

10131

10167

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

0.525

10132

14643

\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=16 x +20 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.525

10133

14681

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

0.525

10134

14683

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

0.525

10135

17776

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

0.525

10136

20607

\begin{align*} \left (-x +3\right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}

0.525

10137

1341

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

0.526

10138

1411

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

0.526

10139

1412

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

0.526

10140

2666

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

0.526

10141

4188

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

0.526

10142

4384

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

0.526

10143

7766

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

0.526

10144

9401

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

0.526

10145

9509

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

0.526

10146

9981

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.526

10147

10615

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

0.526

10148

12511

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

0.526

10149

12936

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

0.526

10150

13065

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

0.526

10151

13884

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

0.526

10152

14943

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

0.526

10153

15443

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

0.526

10154

18666

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

0.526

10155

18855

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.526

10156

19975

\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}

0.526

10157

21748

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

0.526

10158

22273

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

0.526

10159

22638

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

0.526

10160

24721

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

0.526

10161

25197

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

0.526

10162

25529

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

0.526

10163

245

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}

0.527

10164

470

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

0.527

10165

2039

\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.527

10166

4045

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

0.527

10167

7206

\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}

0.527

10168

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*}

0.527

10169

8819

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

0.527

10170

9337

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

0.527

10171

9838

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

0.527

10172

17787

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

0.527

10173

17817

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

0.527

10174

19241

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

0.527

10175

22754

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

0.527

10176

23530

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

0.527

10177

976

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

0.528

10178

2799

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

0.528

10179

4576

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+27 t \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*}

0.528

10180

9210

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

0.528

10181

9679

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

0.528

10182

11006

\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*}

0.528

10183

11671

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

0.528

10184

16969

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

0.528

10185

18095

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

0.528

10186

19637

\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.528

10187

21103

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

0.528

10188

571

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

0.529

10189

979

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

0.529

10190

1094

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

0.529

10191

2043

\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.529

10192

2051

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.529

10193

2053

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

0.529

10194

2466

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

0.529

10195

3857

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

0.529

10196

10525

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

0.529

10197

12958

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

0.529

10198

15777

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

0.529

10199

24043

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

0.529

10200

25353

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

0.529