2.3.2 Problems 101 to 200

Table 2.535: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

101

13123

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

0.029

102

19062

\begin{align*} x^{\prime }&=1+5 y \\ y^{\prime }&=1-6 x^{2} \\ \end{align*}

0.029

103

20209

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

0.029

104

22265

\begin{align*} w^{\prime \prime }-2 z&=0 \\ w^{\prime }+y^{\prime }-z&=2 t \\ w^{\prime }-2 y+z^{\prime \prime }&=0 \\ \end{align*}
With initial conditions
\begin{align*} w \left (0\right ) &= 0 \\ w^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ z^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.029

105

22897

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

0.029

106

22898

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

0.029

107

23778

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

0.029

108

12833

\begin{align*} x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\ \end{align*}

0.030

109

13047

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

0.030

110

13048

\begin{align*} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.030

111

13049

\begin{align*} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.030

112

13093

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

0.030

113

15143

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

0.030

114

18424

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

0.030

115

18707

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

0.030

116

18713

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

0.030

117

21779

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

0.030

118

21780

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

0.030

119

23114

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

0.030

120

23240

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

0.030

121

23263

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

0.030

122

23816

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

0.030

123

23817

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

0.030

124

4555

\begin{align*} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\ x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.031

125

6675

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

0.031

126

6751

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

0.031

127

8153

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

0.031

128

8760

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}

0.031

129

13045

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

0.031

130

13086

\begin{align*} x^{\prime }+x-y^{\prime }&=2 t \\ x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right ) \\ \end{align*}

0.031

131

13131

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

0.031

132

13134

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

0.031

133

13136

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

0.031

134

15130

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

0.031

135

18405

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

0.031

136

18409

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

0.031

137

18712

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

0.031

138

19223

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

0.031

139

22894

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

0.031

140

23255

\begin{align*} x y^{\prime \prime \prime }+4 y^{\prime \prime } x -y x&=1 \\ \end{align*}

0.031

141

6673

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

0.032

142

6792

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

0.032

143

6795

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

0.032

144

8054

\begin{align*} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \\ \end{align*}

0.032

145

9435

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

0.032

146

9438

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

0.032

147

12713

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

0.032

148

13046

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

0.032

149

13099

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

0.032

150

13100

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

0.032

151

13133

\begin{align*} x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }&=2 x y-3 z \\ z^{\prime }&=3 x z-\frac {y^{2}}{6} \\ \end{align*}

0.032

152

15114

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

0.032

153

15146

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

0.032

154

18407

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

0.032

155

18408

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

0.032

156

18425

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

0.032

157

18714

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

0.032

158

19211

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

0.032

159

20810

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

0.032

160

22259

\begin{align*} w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\ -2 w^{\prime }+2 y^{\prime }+z&=0 \\ 2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\ \end{align*}
With initial conditions
\begin{align*} y \left (0\right ) &= 2 \\ z \left (0\right ) &= 2 \\ z^{\prime }\left (0\right ) &= -2 \\ w \left (0\right ) &= 1 \\ w^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.032

161

23776

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

0.032

162

23796

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

0.032

163

23798

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

0.032

164

1469

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

0.033

165

6610

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

0.033

166

6791

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

0.033

167

9437

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

0.033

168

12728

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

0.033

169

12739

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

0.033

170

12773

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

0.033

171

12821

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

0.033

172

13124

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

0.033

173

13127

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

0.033

174

14089

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

0.033

175

14165

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

0.033

176

14346

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

0.033

177

18426

\begin{align*} {\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\ \end{align*}

0.033

178

18706

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

0.033

179

19061

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

0.033

180

20676

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

0.033

181

21250

\begin{align*} x^{\prime }&=2 x-7 x y-a x \\ y^{\prime }&=-y+4 x y-a y \\ \end{align*}

0.033

182

21251

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

0.033

183

21733

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

0.033

184

22892

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

0.033

185

23259

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

0.033

186

23932

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

0.033

187

9436

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

0.034

188

12737

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

0.034

189

14173

\begin{align*} x^{2} y^{\prime \prime \prime }-5 y^{\prime \prime } x +\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \\ \end{align*}

0.034

190

15126

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

0.034

191

15754

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

0.034

192

18143

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

0.034

193

18403

\begin{align*} x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\ \end{align*}

0.034

194

18404

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

0.034

195

18710

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

0.034

196

18717

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

0.034

197

19224

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

0.034

198

23797

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

0.034

199

25360

\begin{align*} y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\ y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\ \end{align*}

0.034

200

8091

\begin{align*} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.035