2.3.12 Problems 1101 to 1200

Table 2.555: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

1101

11178

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

0.075

1102

11276

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

0.075

1103

12797

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

0.075

1104

15138

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

0.075

1105

16813

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

0.075

1106

17546

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

0.075

1107

17552

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y&=0 \\ \end{align*}

0.075

1108

17558

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

0.075

1109

17559

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

0.075

1110

17562

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

0.075

1111

21957

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

0.075

1112

22239

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

0.075

1113

22670

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

0.075

1114

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*}

0.075

1115

24608

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

0.075

1116

25639

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

0.075

1117

264

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}

0.076

1118

492

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

0.076

1119

936

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

0.076

1120

947

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

0.076

1121

1476

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

0.076

1122

3085

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

0.076

1123

3089

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

0.076

1124

3108

\begin{align*} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \\ \end{align*}

0.076

1125

3616

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

0.076

1126

6638

\begin{align*} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

0.076

1127

11245

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

0.076

1128

11277

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

0.076

1129

15677

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y&=0 \\ \end{align*}

0.076

1130

17553

\begin{align*} y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y&=0 \\ \end{align*}

0.076

1131

17554

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

0.076

1132

21177

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

0.076

1133

22784

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

0.076

1134

23232

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

0.076

1135

24553

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

0.076

1136

25642

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

0.076

1137

267

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

0.077

1138

268

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

0.077

1139

307

\begin{align*} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime } \\ y \left (0\right ) &= 18 \\ y^{\prime }\left (0\right ) &= 12 \\ y^{\prime \prime }\left (0\right ) &= 13 \\ y^{\prime \prime \prime }\left (0\right ) &= 7 \\ \end{align*}

0.077

1140

3075

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

0.077

1141

3782

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

0.077

1142

11140

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

0.077

1143

11179

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

0.077

1144

11300

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

0.077

1145

16998

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

0.077

1146

18748

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

0.077

1147

21186

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

0.077

1148

21570

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

0.077

1149

23349

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

0.077

1150

24466

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 12 \\ \end{align*}

0.077

1151

24633

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

0.077

1152

24682

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

0.077

1153

3081

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\ \end{align*}

0.078

1154

3082

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \\ \end{align*}

0.078

1155

3084

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }&=0 \\ \end{align*}

0.078

1156

6756

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

0.078

1157

10540

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

0.078

1158

11225

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

0.078

1159

11250

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

0.078

1160

11270

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

0.078

1161

12818

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

0.078

1162

15673

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\ \end{align*}

0.078

1163

16420

\begin{align*} y^{\prime \prime \prime }&=y^{\prime \prime } \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}

0.078

1164

18127

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

0.078

1165

18747

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

0.078

1166

21192

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

0.078

1167

23348

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

0.078

1168

24452

\begin{align*} 4 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-23 y^{\prime \prime }+12 y^{\prime }+36 y&=0 \\ \end{align*}

0.078

1169

24683

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

0.078

1170

3076

\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y&=0 \\ \end{align*}

0.079

1171

3077

\begin{align*} 12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}

0.079

1172

3102

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

0.079

1173

3104

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

0.079

1174

8952

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}

0.079

1175

8959

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

0.079

1176

10492

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

0.079

1177

10541

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

0.079

1178

10894

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

0.079

1179

10913

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

0.079

1180

10961

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

0.079

1181

11100

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

0.079

1182

11102

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

0.079

1183

12814

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

0.079

1184

13054

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

0.079

1185

13114

\begin{align*} x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\ x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\ x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\ x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \\ \end{align*}

0.079

1186

18464

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

0.079

1187

18571

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

0.079

1188

21311

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

0.079

1189

21895

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

0.079

1190

21981

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

0.079

1191

22244

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.079

1192

23305

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

0.079

1193

23352

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

0.079

1194

312

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

0.080

1195

425

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

0.080

1196

2144

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

0.080

1197

3086

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

0.080

1198

3787

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

0.080

1199

10782

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

0.080

1200

10902

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

0.080