2.3.32 Problems 3101 to 3200

Table 2.607: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3101

1758

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

0.210

3102

2216

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

0.210

3103

7212

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

0.210

3104

9307

\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}

0.210

3105

10784

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

0.210

3106

10807

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

0.210

3107

11052

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}

0.210

3108

11064

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

0.210

3109

12778

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

0.210

3110

18345

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

0.210

3111

20104

\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.210

3112

20888

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

0.210

3113

22779

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

0.210

3114

26042

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

0.210

3115

1277

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}

0.211

3116

1279

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

0.211

3117

3939

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

0.211

3118

7270

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

0.211

3119

9229

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

0.211

3120

10947

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}

0.211

3121

11035

\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*}

0.211

3122

12347

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

0.211

3123

13138

\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.211

3124

13172

\(\left [\begin {array}{cc} 5 & -4 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.211

3125

15011

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

0.211

3126

15475

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

0.211

3127

15686

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=6 x -20-120 \,{\mathrm e}^{x} x^{2} \\ \end{align*}

0.211

3128

17582

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=1 \\ \end{align*}

0.211

3129

19190

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

0.211

3130

19787

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

0.211

3131

21960

\begin{align*} b^{\left (7\right )}&=3 p \\ \end{align*}

0.211

3132

24502

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\infty \right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ \end{align*}

0.211

3133

4117

\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \\ \end{align*}

0.212

3134

8630

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.212

3135

12829

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

0.212

3136

13139

\(\left [\begin {array}{cc} 5 & -6 \\ 3 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.212

3137

18018

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

0.212

3138

21890

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

0.212

3139

22313

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

0.212

3140

419

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

0.213

3141

2108

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

0.213

3142

2191

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

0.213

3143

6603

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

0.213

3144

10552

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

0.213

3145

10927

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

0.213

3146

10950

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

0.213

3147

11010

\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

0.213

3148

11072

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

0.213

3149

18718

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

0.213

3150

21939

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

0.213

3151

22320

\begin{align*} y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\ y \left (0\right ) &= -4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}

0.213

3152

22784

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

0.213

3153

155

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

0.214

3154

1308

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}

0.214

3155

2166

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y&=-{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \\ \end{align*}

0.214

3156

2184

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

0.214

3157

8163

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}

0.214

3158

10572

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

0.214

3159

10863

\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}

0.214

3160

10964

\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}

0.214

3161

10987

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}

0.214

3162

11071

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}

0.214

3163

11149

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

0.214

3164

11162

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

0.214

3165

11167

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

0.214

3166

13143

\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.214

3167

13144

\(\left [\begin {array}{cc} 10 & -8 \\ 6 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.214

3168

14591

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\ \end{align*}

0.214

3169

14595

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \\ \end{align*}

0.214

3170

14616

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}

0.214

3171

16580

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\ \end{align*}

0.214

3172

17576

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}

0.214

3173

17599

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \\ \end{align*}

0.214

3174

17601

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

0.214

3175

19599

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

0.214

3176

20383

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

0.214

3177

380

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

0.215

3178

1306

\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ \end{align*}

0.215

3179

2217

\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ y^{\prime \prime }\left (0\right ) &= -17 \\ \end{align*}

0.215

3180

7948

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

0.215

3181

13176

\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\)

N/A

N/A

N/A

0.215

3182

14617

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y&=0 \\ \end{align*}

0.215

3183

18085

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

0.215

3184

20094

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

0.215

3185

20847

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

0.215

3186

21582

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

0.215

3187

2170

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \\ \end{align*}

0.216

3188

7231

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

0.216

3189

8122

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

0.216

3190

10772

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

0.216

3191

10786

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

0.216

3192

11137

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

0.216

3193

13141

\(\left [\begin {array}{cc} 4 & -3 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.216

3194

15516

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

0.216

3195

19572

\begin{align*} y^{\prime \prime \prime \prime }&=\frac {1}{x^{3}} \\ \end{align*}

0.216

3196

19768

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

0.216

3197

22479

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

0.216

3198

549

\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.217

3199

1042

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

0.217

3200

1486

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

0.217