2.3.2 Problems 101 to 200

Table 2.577: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

101

13081

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

0.037

102

15130

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

0.037

103

23932

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

0.037

104

26750

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

0.037

105

26770

\begin{align*} x^{\prime }&=3 x-22 \sin \left (y\right )+x^{2}-y^{3} \\ y^{\prime }&=\sin \left (x\right )-5 y+{\mathrm e}^{x^{2}}-1 \\ \end{align*}

0.037

106

27701

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

0.037

107

2815

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

0.038

108

13101

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

0.038

109

13129

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

0.038

110

14832

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

0.038

111

25172

\begin{align*} y_{1}^{\prime \prime }+2 y_{1}^{\prime }+6 y_{1}&=5 y_{2} \\ y_{2}^{\prime \prime }-2 y_{2}^{\prime }+6 y_{2}&=9 y_{1} \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{1}^{\prime }\left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 6 \\ y_{2}^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.038

112

26769

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

0.038

113

1469

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

0.039

114

2811

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

0.039

115

3832

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

0.039

116

8198

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

0.039

117

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 \(x=0\).

0.039

118

12825

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

0.039

119

13078

\begin{align*} x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right ) \\ y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right ) \\ \end{align*}

0.039

120

13094

\begin{align*} x^{\prime \prime }+6 x+7 y&=0 \\ y^{\prime \prime }+3 x+2 y&=2 t \\ \end{align*}

0.039

121

13119

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

0.039

122

13121

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

0.039

123

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*}

0.039

124

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*}

0.039

125

14166

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

0.039

126

15129

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

0.039

127

19543

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

0.039

128

20810

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

0.039

129

23107

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

0.039

130

23440

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

Series expansion around \(x=0\).

0.039

131

23441

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

Series expansion around \(x=0\).

0.039

132

23782

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

0.039

133

25358

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

0.039

134

26776

\begin{align*} x^{\prime }&=\frac {{\mathrm e}^{x}}{4}-\frac {1}{4}-9 y+x^{4} \\ y^{\prime }&=\frac {x}{5}-\sin \left (y\right )+y^{14} \\ \end{align*}

0.039

135

27198

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

0.039

136

2792

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

0.040

137

2813

\begin{align*} x^{\prime }&=x-x^{3}-x y \\ y^{\prime }&=2 y-y^{5}-y \,x^{4} \\ \end{align*}

0.040

138

2816

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

0.040

139

2818

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

0.040

140

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 \(x=0\).

0.040

141

9438

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

Series expansion around \(x=0\).

0.040

142

12730

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

0.040

143

13047

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

0.040

144

13048

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

0.040

145

13085

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

0.040

146

17824

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

0.040

147

19225

\begin{align*} x^{\prime } t +6 x-y-3 z&=0 \\ t y^{\prime }+23 x-6 y-9 z&=0 \\ z^{\prime } t +x+y-2 z&=0 \\ \end{align*}

0.040

148

20991

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

0.040

149

21238

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

0.040

150

23114

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

0.040

151

26768

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

0.040

152

26772

\begin{align*} x^{\prime }&=7 x+2 \sin \left (y\right )-4 y^{4} \\ y^{\prime }&={\mathrm e}^{x}-3 y-1+\frac {5 x^{2}}{2} \\ \end{align*}

0.040

153

1463

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

0.041

154

1470

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

0.041

155

12740

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

0.041

156

13045

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

0.041

157

13095

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

0.041

158

13131

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

0.041

159

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*}

0.041

160

14173

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

0.041

161

21001

\begin{align*} w_{1}^{\prime }&=w_{2} \\ w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\ \end{align*}

0.041

162

22257

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

With initial conditions

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

0.041

163

23263

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

0.041

164

26135

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

0.041

165

608

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

0.042

166

7056

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

0.042

167

12728

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

0.042

168

12733

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

0.042

169

12737

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

0.042

170

12767

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

0.042

171

12831

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

0.042

172

13049

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

0.042

173

14165

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

0.042

174

18635

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

0.042

175

23265

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

0.042

176

26773

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

0.042

177

26786

\begin{align*} y^{\prime \prime \prime \prime }+11 y^{\prime \prime \prime }+41 y^{\prime \prime }+61 y^{\prime }+30 y&=0 \\ \end{align*}

0.042

178

26793

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

0.042

179

944

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

0.043

180

2789

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

0.043

181

3091

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

0.043

182

3890

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

0.043

183

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*}

0.043

184

9485

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

With initial conditions

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

0.043

185

12709

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

0.043

186

12744

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

0.043

187

12780

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

0.043

188

17422

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

0.043

189

18634

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

0.043

190

20992

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

0.043

191

21236

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

0.043

192

21317

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

0.043

193

23241

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

0.043

194

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*}

0.043

195

26775

\begin{align*} x^{\prime }&=\frac {3 \sin \left (x\right )}{4}-7 y \left (1-y\right )^{{1}/{3}}+x^{3} \\ y^{\prime }&=\frac {2 x}{3}-3 y \cos \left (y\right )-11 y^{5} \\ \end{align*}

0.043

196

4557

\begin{align*} x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\ 3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\ \end{align*}

With initial conditions

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

0.044

197

7066

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

0.044

198

12773

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

0.044

199

12781

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

0.044

200

12821

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

0.044