Problems 1001 to 1100

Table 4.579: Solved using series method


#	ODE	Mathematica	Maple	Sympy

7243	\[ {} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0 \]	✓	✓	✓

7244	\[ {} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \]	✓	✓	✓

7245	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \]	✓	✓	✓

7246	\[ {} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0 \]	✓	✓	✓

7247	\[ {} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \]	✓	✓	✓

7248	\[ {} x y^{\prime \prime }+2 y^{\prime }-x y = 0 \]	✓	✓	✓

7249	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

7250	\[ {} x y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✓

7251	\[ {} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \]	✓	✓	✓

7252	\[ {} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \]	✓	✓	✓

7253	\[ {} x y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

7254	\[ {} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]	✓	✓	✗

7255	\[ {} x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]	✓	✓	✓

7256	\[ {} x^{4} y^{\prime \prime }+\lambda y = 0 \]	✓	✗	✗

7257	\[ {} x^{3} y^{\prime \prime }+y = 0 \]	✓	✗	✗

7258	\[ {} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]	✓	✗	✗

7259	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]	✓	✓	✓

7260	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \]	✓	✓	✓

7261	\[ {} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]	✓	✓	✓

7262	\[ {} 16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]	✓	✓	✓

7263	\[ {} x y^{\prime \prime }+y^{\prime }+x y = 0 \]	✓	✓	✓

7264	\[ {} y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0 \]	✓	✓	✓

7265	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \]	✓	✓	✓

7266	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

7267	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]	✓	✓	✓

7268	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]	✓	✓	✗

7269	\[ {} x y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]	✓	✓	✓

7270	\[ {} x y^{\prime \prime }+3 y^{\prime }+x y = 0 \]	✓	✓	✓

7271	\[ {} x y^{\prime \prime }-y^{\prime }+x y = 0 \]	✓	✓	✓

7272	\[ {} x y^{\prime \prime }-5 y^{\prime }+x y = 0 \]	✓	✓	✗

7273	\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

7274	\[ {} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \]	✓	✓	✓

7275	\[ {} x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \]	✓	✓	✓

7276	\[ {} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]	✓	✓	✓

7277	\[ {} y^{\prime \prime }-x^{2} y = 0 \]	✓	✓	✓

7278	\[ {} x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \]	✓	✓	✓

7279	\[ {} y^{\prime \prime }+y = 0 \]	✓	✓	✓

7280	\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

7281	\[ {} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]	✓	✓	✓

7282	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y = 0 \]	✓	✓	✓

7283	\[ {} 2 x y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

7284	\[ {} y^{\prime \prime }-x y^{\prime }-y = 0 \]	✓	✓	✓

7285	\[ {} \left (x -1\right ) y^{\prime \prime }+3 y = 0 \]	✓	✓	✓

7286	\[ {} y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \]	✓	✓	✓

7287	\[ {} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

7288	\[ {} \cos \left (x \right ) y^{\prime \prime }+y = 0 \]	✓	✓	✓

7289	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✓

7290	\[ {} \left (x +2\right ) y^{\prime \prime }+3 y = 0 \]	✓	✓	✓

7291	\[ {} \left (1+x \right ) y^{\prime } = y \]	✓	✓	✓

7292	\[ {} y^{\prime } = -2 x y \]	✓	✓	✓

7293	\[ {} x y^{\prime }-3 y = k \]	✓	✓	✗

7294	\[ {} y^{\prime \prime }+y = 0 \]	✓	✓	✓

7295	\[ {} y^{\prime \prime }-y^{\prime }+x y = 0 \]	✓	✓	✓

7296	\[ {} y^{\prime \prime }-y^{\prime }+x^{2} y = 0 \]	✓	✓	✓

7297	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]	✓	✓	✓

7298	\[ {} y^{\prime \prime }+\left (x^{2}+1\right ) y = 0 \]	✓	✓	✓

7299	\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]	✓	✓	✓

7300	\[ {} y^{\prime }+4 y = 1 \]	✓	✓	✓

7301	\[ {} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \]	✓	✓	✓

7302	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]	✓	✓	✓

7303	\[ {} \left (x -2\right ) y^{\prime } = x y \]	✓	✓	✓

7304	\[ {} \left (x -2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = 0 \]	✓	✓	✓

7305	\[ {} x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]	✓	✓	✓

7306	\[ {} x y^{\prime \prime }+y = 0 \]	✓	✓	✓

7307	\[ {} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \]	✓	✓	✓

7308	\[ {} x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

7309	\[ {} y^{\prime \prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

7310	\[ {} x y^{\prime \prime }+y^{\prime }+x y = 0 \]	✓	✓	✓

7311	\[ {} 2 x \left (x -1\right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

7312	\[ {} x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \]	✓	✓	✓

7313	\[ {} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y = 0 \]	✓	✓	✓

7314	\[ {} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]	✓	✓	✓

7315	\[ {} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

7316	\[ {} 2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

7317	\[ {} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

7318	\[ {} 4 x y^{\prime \prime }+y^{\prime }+8 y = 0 \]	✓	✓	✓

7319	\[ {} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

7320	\[ {} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]	✓	✓	✓

7321	\[ {} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]	✓	✓	✓

7322	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y = 0 \]	✓	✓	✓

7323	\[ {} x y^{\prime \prime }+y^{\prime }+\frac {y}{4} = 0 \]	✓	✓	✓

7324	\[ {} y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y = 0 \]	✓	✓	✓

7325	\[ {} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]	✓	✓	✓

7326	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \]	✓	✓	✓

7327	\[ {} \left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x \left (1+x \right ) y = 0 \]	✓	✓	✓

7328	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y = 0 \]	✓	✓	✗

7329	\[ {} x y^{\prime \prime }+5 y^{\prime }+x y = 0 \]	✓	✓	✓

7330	\[ {} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y = 0 \]	✓	✓	✓

7331	\[ {} y^{\prime \prime }+x y = 0 \]	✓	✓	✓

7332	\[ {} 4 x y^{\prime \prime }+4 y^{\prime }+y = 0 \]	✓	✓	✓

7333	\[ {} x y^{\prime \prime }+y^{\prime }+36 y = 0 \]	✓	✓	✓

7334	\[ {} y^{\prime \prime }+k^{2} x^{2} y = 0 \]	✓	✓	✓

7335	\[ {} y^{\prime \prime }+k^{2} x^{4} y = 0 \]	✓	✓	✓

7336	\[ {} x y^{\prime \prime }-5 y^{\prime }+x y = 0 \]	✓	✓	✗

7337	\[ {} y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

7338	\[ {} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

7339	\[ {} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y = 0 \]	✓	✓	✗

7340	\[ {} 16 \left (1+x \right )^{2} y^{\prime \prime }+3 y = 0 \]	✓	✓	✗

7341	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y = 0 \]	✓	✓	✗

7342	\[ {} x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

4.7.11 Problems 1001 to 1100