2.2.12 Problems 1101 to 1200

Table 2.25: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

1101

\[ {}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right ) \]

[_linear]

1.637

1102

\[ {}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

1.368

1103

\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \]

[_linear]

1.506

1104

\[ {}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}} \]

[_linear]

2.727

1105

\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}} \]

[_linear]

2.380

1106

\[ {}y+2 y^{\prime } = 3 t \]

[[_linear, ‘class A‘]]

1.286

1107

\[ {}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t} \]

[_linear]

1.487

1108

\[ {}y+y^{\prime } = 5 \sin \left (2 t \right ) \]

[[_linear, ‘class A‘]]

1.623

1109

\[ {}y+2 y^{\prime } = 3 t^{2} \]

[[_linear, ‘class A‘]]

1.342

1110

\[ {}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t \]
i.c.

[[_linear, ‘class A‘]]

1.643

1111

\[ {}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t} \]
i.c.

[[_linear, ‘class A‘]]

2.129

1112

\[ {}2 y+t y^{\prime } = t^{2}-t +1 \]
i.c.

[_linear]

1.825

1113

\[ {}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}} \]
i.c.

[_linear]

1.724

1114

\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} \]
i.c.

[[_linear, ‘class A‘]]

1.524

1115

\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \]
i.c.

[_linear]

1.895

1116

\[ {}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t} \]
i.c.

[_linear]

1.618

1117

\[ {}\left (t +1\right ) y+t y^{\prime } = t \]
i.c.

[_linear]

1.536

1118

\[ {}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

1.621

1119

\[ {}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}} \]
i.c.

[[_linear, ‘class A‘]]

1.461

1120

\[ {}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}} \]
i.c.

[[_linear, ‘class A‘]]

1.728

1121

\[ {}\left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t} \]
i.c.

[_linear]

2.246

1122

\[ {}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t} \]
i.c.

[_linear]

1.655

1123

\[ {}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t} \]
i.c.

[_linear]

35.893

1124

\[ {}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

1.943

1125

\[ {}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2} \]

[[_linear, ‘class A‘]]

1.332

1126

\[ {}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right ) \]
i.c.

[[_linear, ‘class A‘]]

2.187

1127

\[ {}-y+y^{\prime } = 1+3 \sin \left (t \right ) \]

[[_linear, ‘class A‘]]

1.712

1128

\[ {}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t \]

[[_linear, ‘class A‘]]

1.499

1129

\[ {}y^{\prime } = \frac {x^{2}}{y} \]

[_separable]

2.191

1130

\[ {}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y} \]

[_separable]

1.901

1131

\[ {}\sin \left (x \right ) y^{2}+y^{\prime } = 0 \]

[_separable]

1.918

1132

\[ {}y^{\prime } = \frac {3 x^{2}-1}{3+2 y} \]

[_separable]

1.737

1133

\[ {}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \]

[_separable]

2.527

1134

\[ {}x y^{\prime } = \sqrt {1-y^{2}} \]

[_separable]

6.326

1135

\[ {}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \]

[‘y=_G(x,y’)‘]

1.895

1136

\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \]

[_separable]

1.292

1137

\[ {}y^{\prime } = \left (1-2 x \right ) y^{2} \]
i.c.

[_separable]

2.308

1138

\[ {}y^{\prime } = \frac {1-2 x}{y} \]
i.c.

[_separable]

3.910

1139

\[ {}x +y y^{\prime } {\mathrm e}^{-x} = 0 \]
i.c.

[_separable]

4.357

1140

\[ {}r^{\prime } = \frac {r^{2}}{x} \]
i.c.

[_separable]

2.108

1141

\[ {}y^{\prime } = \frac {2 x}{y+x^{2} y} \]
i.c.

[_separable]

2.369

1142

\[ {}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}} \]
i.c.

[_separable]

2.900

1143

\[ {}y^{\prime } = \frac {2 x}{2 y+1} \]
i.c.

[_separable]

3.499

1144

\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \]
i.c.

[_separable]

2.975

1145

\[ {}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \]
i.c.

[_separable]

3.338

1146

\[ {}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \]
i.c.

[_separable]

4.533

1147

\[ {}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \]
i.c.

[_separable]

38.986

1148

\[ {}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right ) \]
i.c.

[_separable]

3.368

1149

\[ {}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \]
i.c.

[_separable]

4.862

1150

\[ {}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \]
i.c.

[_separable]

3.079

1151

\[ {}y^{\prime } = 2 y^{2}+x y^{2} \]
i.c.

[_separable]

2.368

1152

\[ {}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y} \]
i.c.

[_separable]

3.632

1153

\[ {}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y} \]
i.c.

[_separable]

14.723

1154

\[ {}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right ) \]
i.c.

[_separable]

2.763

1155

\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \]

[_separable]

2.609

1156

\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \]

[_separable]

3.117

1157

\[ {}y^{\prime } = \frac {b +a y}{d +c y} \]

[_quadrature]

1.974

1158

\[ {}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

2.514

1159

\[ {}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6.937

1160

\[ {}y^{\prime } = \frac {4 y-3 x}{2 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.009

1161

\[ {}y^{\prime } = -\frac {4 x +3 y}{2 x +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.078

1162

\[ {}y^{\prime } = \frac {x +3 y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.358

1163

\[ {}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

2.224

1164

\[ {}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

57.382

1165

\[ {}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

120.224

1166

\[ {}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t \]

[_linear]

2.099

1167

\[ {}y+\left (-4+t \right ) t y^{\prime } = 0 \]
i.c.

[_separable]

2.068

1168

\[ {}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right ) \]
i.c.

[_linear]

2.036

1169

\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \]
i.c.

[_linear]

2.257

1170

\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \]
i.c.

[_linear]

2.095

1171

\[ {}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right ) \]

[_linear]

1.830

1172

\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \]

[_separable]

1.446

1173

\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1} \]

[_separable]

1.897

1174

\[ {}y^{\prime } = -\frac {4 t}{y} \]

[_separable]

4.111

1175

\[ {}y^{\prime } = 2 t y^{2} \]

[_separable]

2.123

1176

\[ {}y^{3}+y^{\prime } = 0 \]

[_quadrature]

5.093

1177

\[ {}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \]

[_separable]

1.912

1178

\[ {}y^{\prime } = t \left (3-y\right ) y \]

[_separable]

2.583

1179

\[ {}y^{\prime } = y \left (3-t y\right ) \]

[_Bernoulli]

1.844

1180

\[ {}y^{\prime } = -y \left (3-t y\right ) \]

[_Bernoulli]

1.840

1181

\[ {}y^{\prime } = t -1-y^{2} \]

[_Riccati]

1.188

1182

\[ {}y^{\prime } = a y+b y^{2} \]

[_quadrature]

3.731

1183

\[ {}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right ) \]

[_quadrature]

3.837

1184

\[ {}y^{\prime } = -1+{\mathrm e}^{y} \]

[_quadrature]

2.342

1185

\[ {}y^{\prime } = -1+{\mathrm e}^{-y} \]

[_quadrature]

2.245

1186

\[ {}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}} \]

[_quadrature]

4.915

1187

\[ {}y^{\prime } = -k \left (-1+y\right )^{2} \]

[_quadrature]

1.208

1188

\[ {}y^{\prime } = y^{2} \left (-1+y^{2}\right ) \]

[_quadrature]

1.734

1189

\[ {}y^{\prime } = y \left (1-y^{2}\right ) \]

[_quadrature]

4.331

1190

\[ {}y^{\prime } = -b \sqrt {y}+a y \]

[_quadrature]

4.172

1191

\[ {}y^{\prime } = y^{2} \left (4-y^{2}\right ) \]

[_quadrature]

1.845

1192

\[ {}y^{\prime } = \left (1-y\right )^{2} y^{2} \]

[_quadrature]

1.829

1193

\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \]

[_separable]

2.944

1194

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5.551

1195

\[ {}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0 \]

[_exact, _rational]

1.369

1196

\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \]

[_separable]

2.209

1197

\[ {}y^{\prime } = \frac {-a x -b y}{b x +c y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.211

1198

\[ {}y^{\prime } = \frac {-a x +b y}{b x -c y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.568

1199

\[ {}{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \]

[_exact]

7.007

1200

\[ {}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0 \]

[‘x=_G(y,y’)‘]

9.158