Problems 1 to 100

Table 4.1011: Second or higher order ODE with non-constant coeﬃcients


#	ODE	Mathematica	Maple	Sympy

147	\[ {} x y^{\prime \prime } = y^{\prime } \]	✓	✓	✓

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

150	\[ {} x y^{\prime \prime }+y^{\prime } = 4 x \]	✓	✓	✓

151	\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \]	✓	✓	✓

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

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

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

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

156	\[ {} y^{3} y^{\prime \prime } = 1 \]	✓	✓	✓

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

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

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

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

228	\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]	✓	✓	✓

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

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

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

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

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

245	\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]	✓	✓	✓

246	\[ {} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \]	✓	✓	✓

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

248	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]	✓	✓	✓

255	\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]	✓	✓	✓

256	\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]	✓	✓	✓

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

264	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]	✓	✓	✓

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

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

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

315	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]	✓	✓	✓

316	\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \]	✓	✓	✓

317	\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \]	✓	✓	✓

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

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

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

321	\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]	✓	✓	✓

376	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]	✓	✓	✓

377	\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \]	✓	✓	✓

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

379	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}} \]	✓	✓	✓

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

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

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

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

516	\[ {} x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0 \]	✓	✓	✓

517	\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (x +8\right ) y = 0 \]	✓	✓	✓

518	\[ {} 36 x^{2} y^{\prime \prime }+60 x y^{\prime }+\left (9 x^{3}-5\right ) y = 0 \]	✓	✓	✓

519	\[ {} 16 x^{2} y^{\prime \prime }+24 x y^{\prime }+\left (144 x^{3}+1\right ) y = 0 \]	✓	✓	✓

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

521	\[ {} 4 x^{2} y^{\prime \prime }-12 x y^{\prime }+\left (15+16 x \right ) y = 0 \]	✓	✓	✓

522	\[ {} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y = 0 \]	✓	✓	✓

523	\[ {} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-2 \left (-x^{5}+14\right ) y = 0 \]	✓	✓	✓

524	\[ {} y^{\prime \prime }+x^{4} y = 0 \]	✓	✓	✓

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

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

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

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

557	\[ {} t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (1+2 t \right ) x = 0 \]	✓	✓	✓

558	\[ {} t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x = 0 \]	✓	✓	✓

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

560	\[ {} t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x = 0 \]	✓	✓	✓

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

820	\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]	✓	✓	✓

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

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

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

834	\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]	✓	✓	✓

835	\[ {} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \]	✓	✓	✓

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

837	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]	✓	✓	✓

860	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]	✓	✓	✓

861	\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \]	✓	✓	✓

902	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]	✓	✓	✓

903	\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \]	✓	✓	✓

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

905	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}} \]	✓	✓	✓

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

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

928	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]	✓	✓	✓

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

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

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

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

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

958	\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \]	✓	✓	✓

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

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

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

962	\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]	✓	✓	✓

1293	\[ {} t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \]	✓	✓	✓

1294	\[ {} t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \]	✓	✓	✓

1295	\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0 \]	✓	✓	✓

1296	\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \]	✓	✓	✓

1297	\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]	✓	✓	✓

1298	\[ {} t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0 \]	✓	✓	✓

1299	\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0 \]	✓	✓	✓

4.24.1 Problems 1 to 100