Problems 1 to 100

Table 5.35: Problems not solved by Sympy


#	ODE	Mathematica	Maple	Sympy

28	\[ {} y^{\prime } = x \ln \left (y\right ) \]	✓	✓	✗

29	\[ {} y^{\prime } = y^{{1}/{3}} \]	✓	✓	✗

32	\[ {} y^{\prime } = \sqrt {x -y} \]	✓	✓	✗

36	\[ {} y^{\prime } = -y^{2}+x^{2} \]	✓	✓	✗

39	\[ {} y^{\prime } = x^{2}+y^{2}-1 \]	✓	✗	✗

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

47	\[ {} y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}} \]	✓	✓	✗

54	\[ {} y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \]	✓	✓	✗

55	\[ {} y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \]	✓	✓	✗

70	\[ {} {y^{\prime }}^{2} = 4 y \]	✓	✓	✗

71	\[ {} y^{\prime } = 2 \sqrt {y} \]	✓	✓	✗

97	\[ {} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \]	✓	✓	✗

112	\[ {} y^{\prime } x^{2} = x y+x^{2} {\mathrm e}^{\frac {y}{x}} \]	✓	✓	✗

116	\[ {} x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \]	✓	✓	✗

132	\[ {} x \,{\mathrm e}^{y} y^{\prime } = 2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \]	✓	✓	✗

137	\[ {} 3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

138	\[ {} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

139	\[ {} x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

140	\[ {} 1+y \,{\mathrm e}^{x y}+\left (2 y+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \]	✓	✓	✗

141	\[ {} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0 \]	✓	✓	✗

142	\[ {} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0 \]	✓	✓	✗

143	\[ {} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

144	\[ {} {\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

145	\[ {} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0 \]	✗	✓	✗

146	\[ {} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0 \]	✓	✓	✗

148	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

153	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime } \]	✓	✓	✗

155	\[ {} y^{\prime \prime } = 2 {y^{\prime }}^{3} y \]	✓	✓	✗

157	\[ {} y^{\prime \prime } = 2 y y^{\prime } \]	✓	✓	✗

158	\[ {} y y^{\prime \prime } = 3 {y^{\prime }}^{2} \]	✓	✓	✗

161	\[ {} y^{\prime }+p \left (x \right ) y = q \left (x \right ) y \ln \left (y\right ) \]	✓	✓	✗

167	\[ {} y^{\prime }+y^{2} = x^{2}+1 \]	✓	✓	✗

170	\[ {} r y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

173	\[ {} x^{\prime } = 1-x^{2} \]	✓	✓	✗

174	\[ {} x^{\prime } = 9-4 x^{2} \]	✓	✓	✗

182	\[ {} 2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

190	\[ {} 6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

195	\[ {} {\mathrm e}^{x}+y \,{\mathrm e}^{x y}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \]	✓	✓	✗

201	\[ {} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

204	\[ {} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]	✗	✓	✗

232	\[ {} y y^{\prime \prime } = 6 x^{4} \]	✗	✗	✗

233	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

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

267	\[ {} \left (1+x \right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0 \]	✓	✓	✗

268	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]	✓	✓	✗

269	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]	✓	✓	✗

314	\[ {} a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y = 0 \]	✓	✓	✗

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

413	\[ {} y^{\prime \prime }+y = x \]	✓	✓	✗

414	\[ {} x y^{\prime }+y = 0 \]	✓	✓	✗

415	\[ {} 2 x y^{\prime } = y \]	✓	✓	✗

416	\[ {} y^{\prime } x^{2}+y = 0 \]	✓	✗	✗

417	\[ {} x^{3} y^{\prime } = 2 y \]	✓	✗	✗

422	\[ {} x^{2} y^{\prime \prime }+y^{\prime } x^{2}+y = 0 \]	✓	✓	✗

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

460	\[ {} 3 x^{3} y^{\prime \prime }+2 y^{\prime } x^{2}+\left (-x^{2}+1\right ) y = 0 \]	✓	✗	✗

463	\[ {} x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y = 0 \]	✓	✓	✗

472	\[ {} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0 \]	✓	✗	✗

490	\[ {} 2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y = 0 \]	✓	✓	✗

491	\[ {} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]	✓	✗	✗

492	\[ {} x^{3} y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✗	✗

495	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y = 0 \]	✓	✓	✗

497	\[ {} x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0 \]	✓	✓	✗

502	\[ {} x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y = 0 \]	✓	✓	✗

525	\[ {} x y^{\prime \prime }+4 x^{3} y = 0 \]	✓	✓	✗

527	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✗

528	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✗

529	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✗

555	\[ {} t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x = 0 \]	✓	✓	✗

556	\[ {} t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x = 0 \]	✓	✓	✗

559	\[ {} t x^{\prime \prime }-2 x^{\prime }+t x = 0 \]	✓	✓	✗

604	\[ {} [x^{\prime }\left (t \right ) = t x \left (t \right )-{\mathrm e}^{t} y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+t^{2} y \left (t \right )-\sin \left (t \right )] \]	✗	✓	✗

606	\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 5 y \left (t \right )-7 z \left (t \right )] \]	✓	✓	✗

607	\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+t, y^{\prime }\left (t \right ) = x \left (t \right )-3 z \left (t \right )+t^{2}, z^{\prime }\left (t \right ) = 6 y \left (t \right )-7 z \left (t \right )+t^{3}] \]	✓	✓	✗

608	\[ {} [x^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right )] \]	✗	✗	✗

671	\[ {} y^{\prime } = y^{{1}/{3}} \]	✓	✓	✗

676	\[ {} y^{\prime } = -y^{2}+x^{2} \]	✓	✓	✗

683	\[ {} y^{\prime } = 4 \left (x y\right )^{{1}/{3}} \]	✓	✓	✗

689	\[ {} y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \]	✓	✓	✗

690	\[ {} y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \]	✓	✓	✗

728	\[ {} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \]	✓	✓	✗

736	\[ {} y^{\prime } x^{2} = x y+x^{2} {\mathrm e}^{\frac {y}{x}} \]	✓	✓	✗

740	\[ {} x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \]	✓	✓	✗

756	\[ {} x \,{\mathrm e}^{y} y^{\prime } = 2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \]	✓	✓	✗

761	\[ {} 3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

762	\[ {} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

763	\[ {} x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

764	\[ {} 1+y \,{\mathrm e}^{x y}+\left (2 y+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \]	✓	✓	✗

765	\[ {} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0 \]	✓	✓	✗

766	\[ {} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0 \]	✓	✓	✗

767	\[ {} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

768	\[ {} {\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

769	\[ {} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0 \]	✗	✓	✗

770	\[ {} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0 \]	✓	✓	✗

774	\[ {} 2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

782	\[ {} 6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

783	\[ {} y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4} \]	✗	✗	✗

787	\[ {} {\mathrm e}^{x}+y \,{\mathrm e}^{x y}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \]	✓	✓	✗

793	\[ {} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

796	\[ {} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]	✗	✓	✗

5.3.1 Problems 1 to 100