Problems 201 to 300

Table 4.549: Second ODE homogeneous ODE


#	ODE	Mathematica	Maple	Sympy

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

1300	\[ {} t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0 \]	✓	✓	✓

1301	\[ {} y^{\prime \prime }+t y^{\prime }+y \,{\mathrm e}^{-t^{2}} = 0 \]	✓	✓	✗

1302	\[ {} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \]	✓	✓	✗

1303	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

1304	\[ {} 9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]	✓	✓	✓

1305	\[ {} 4 y^{\prime \prime }-4 y^{\prime }-3 y = 0 \]	✓	✓	✓

1306	\[ {} 4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \]	✓	✓	✓

1307	\[ {} y^{\prime \prime }-2 y^{\prime }+10 y = 0 \]	✓	✓	✓

1308	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]	✓	✓	✓

1309	\[ {} 4 y^{\prime \prime }+17 y^{\prime }+4 y = 0 \]	✓	✓	✓

1310	\[ {} 16 y^{\prime \prime }+24 y^{\prime }+9 y = 0 \]	✓	✓	✓

1311	\[ {} 25 y^{\prime \prime }-20 y^{\prime }+4 y = 0 \]	✓	✓	✓

1312	\[ {} 2 y^{\prime \prime }+2 y^{\prime }+y = 0 \]	✓	✓	✓

1313	\[ {} 9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]	✓	✓	✓

1314	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]	✓	✓	✓

1315	\[ {} 9 y^{\prime \prime }+6 y^{\prime }+82 y = 0 \]	✓	✓	✓

1316	\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]	✓	✓	✓

1317	\[ {} 4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \]	✓	✓	✓

1318	\[ {} y^{\prime \prime }-y^{\prime }+\frac {y}{4} = 0 \]	✓	✓	✓

1319	\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]	✓	✓	✓

1320	\[ {} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0 \]	✓	✓	✓

1321	\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]	✓	✓	✓

1322	\[ {} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0 \]	✓	✓	✗

1323	\[ {} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]	✓	✓	✓

1324	\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✗

1325	\[ {} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]	✓	✓	✓

1326	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

1327	\[ {} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \]	✓	✓	✓

1328	\[ {} t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4} = 0 \]	✓	✓	✓

1329	\[ {} 2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \]	✓	✓	✓

1330	\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]	✓	✓	✓

1331	\[ {} 4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0 \]	✓	✓	✓

1332	\[ {} t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0 \]	✓	✓	✓

1355	\[ {} u^{\prime \prime }+2 u = 0 \]	✓	✓	✓

1356	\[ {} u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0 \]	✓	✓	✓

1483	\[ {} y^{\prime \prime }-y^{\prime }-6 y = 0 \]	✓	✓	✓

1484	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]	✓	✓	✓

1485	\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]	✓	✓	✓

1486	\[ {} y^{\prime \prime }-2 y^{\prime }+4 y = 0 \]	✓	✓	✓

1487	\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]	✓	✓	✓

1737	\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]	✓	✓	✓

1738	\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]	✓	✓	✓

1739	\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]	✓	✓	✓

1740	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

1741	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

1742	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]	✓	✓	✗

1743	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]	✓	✓	✓

1744	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]	✓	✓	✓

1745	\[ {} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]	✓	✓	✓

1746	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]	✓	✓	✓

1747	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✓

1748	\[ {} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0 \]	✓	✓	✓

1749	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]	✓	✓	✓

1750	\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✗

1751	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

1752	\[ {} 4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+x \cos \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y = 0 \]	✓	✓	✗

1753	\[ {} \left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\left (6 x -8\right ) y = 0 \]	✓	✓	✗

1754	\[ {} \left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]	✓	✓	✗

1755	\[ {} \left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0 \]	✗	✓	✗

1756	\[ {} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (-2+2 x \right ) y = 0 \]	✓	✓	✗

1774	\[ {} x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0 \]	✓	✓	✗

1775	\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]	✓	✓	✓

1776	\[ {} x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-2 x \ln \left (x \right ) y^{\prime }+\left (2+\ln \left (x \right )\right ) y = 0 \]	✓	✓	✗

1777	\[ {} 4 x y^{\prime \prime }+2 y^{\prime }+y = 0 \]	✓	✓	✓

1778	\[ {} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0 \]	✓	✓	✗

1779	\[ {} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0 \]	✓	✓	✓

1780	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

1781	\[ {} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \]	✓	✓	✗

1782	\[ {} 4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+x \cos \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y = 0 \]	✓	✓	✗

1783	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]	✓	✓	✓

1784	\[ {} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0 \]	✓	✓	✗

1785	\[ {} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (-2+2 x \right ) y = 0 \]	✓	✓	✗

1786	\[ {} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \]	✓	✓	✗

1788	\[ {} \left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]	✓	✓	✗

2362	\[ {} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]	✓	✓	✓

2363	\[ {} y^{\prime \prime }+t y^{\prime }+y = 0 \]	✓	✓	✗

2364	\[ {} y^{\prime \prime }-y = 0 \]	✓	✓	✓

2365	\[ {} 6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]	✓	✓	✓

2366	\[ {} y^{\prime \prime }-3 y^{\prime }+y = 0 \]	✓	✓	✓

2367	\[ {} 3 y^{\prime \prime }+6 y^{\prime }+3 y = 0 \]	✓	✓	✓

2368	\[ {} y^{\prime \prime }-3 y^{\prime }-4 y = 0 \]	✓	✓	✓

2369	\[ {} 2 y^{\prime \prime }+y^{\prime }-10 y = 0 \]	✓	✓	✓

2370	\[ {} 5 y^{\prime \prime }+5 y^{\prime }-y = 0 \]	✓	✓	✓

2371	\[ {} y^{\prime \prime }-6 y^{\prime }+y = 0 \]	✓	✓	✓

2372	\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]	✓	✓	✓

2373	\[ {} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0 \]	✓	✓	✓

2374	\[ {} t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \]	✓	✓	✓

2375	\[ {} t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0 \]	✓	✓	✓

2376	\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]	✓	✓	✓

2377	\[ {} y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

2378	\[ {} 2 y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]	✓	✓	✓

2379	\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]	✓	✓	✓

2380	\[ {} 4 y^{\prime \prime }-y^{\prime }+y = 0 \]	✓	✓	✓

2381	\[ {} y^{\prime \prime }+y^{\prime }+2 y = 0 \]	✓	✓	✓

2382	\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]	✓	✓	✓

4.4.3 Problems 201 to 300