Problems 1001 to 1100

Table 4.769: Solved using series method


#	ODE	Mathematica	Maple	Sympy

8529	\[ {} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0 \]	✓	✓	✓

8530	\[ {} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \]	✓	✓	✓

8531	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \]	✓	✓	✓

8532	\[ {} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0 \]	✓	✓	✓

8533	\[ {} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \]	✓	✓	✓

8534	\[ {} -x y+2 y^{\prime }+x y^{\prime \prime } = 0 \]	✓	✓	✓

8535	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

8536	\[ {} x y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✓

8537	\[ {} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \]	✓	✓	✓

8538	\[ {} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \]	✓	✓	✓

8539	\[ {} x y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

8540	\[ {} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]	✓	✓	✗

8541	\[ {} x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]	✓	✓	✓

8542	\[ {} x^{4} y^{\prime \prime }+\lambda y = 0 \]	✓	✗	✗

8543	\[ {} x^{3} y^{\prime \prime }+y = 0 \]	✓	✗	✗

8544	\[ {} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]	✓	✗	✗

8545	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]	✓	✓	✓

8546	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0 \]	✓	✓	✓

8547	\[ {} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]	✓	✓	✓

8548	\[ {} 16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]	✓	✓	✓

8549	\[ {} x y^{\prime \prime }+y^{\prime }+x y = 0 \]	✓	✓	✓

8550	\[ {} y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0 \]	✓	✓	✓

8551	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \]	✓	✓	✓

8552	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

8553	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]	✓	✓	✓

8554	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]	✓	✓	✗

8555	\[ {} x y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]	✓	✓	✓

8556	\[ {} x y^{\prime \prime }+3 y^{\prime }+x y = 0 \]	✓	✓	✓

8557	\[ {} x y^{\prime \prime }-y^{\prime }+x y = 0 \]	✓	✓	✓

8558	\[ {} x y^{\prime \prime }-5 y^{\prime }+x y = 0 \]	✓	✓	✗

8559	\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

8560	\[ {} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \]	✓	✓	✓

8561	\[ {} x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \]	✓	✓	✓

8562	\[ {} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]	✓	✓	✓

8563	\[ {} y^{\prime \prime }-x^{2} y = 0 \]	✓	✓	✓

8564	\[ {} x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \]	✓	✓	✓

8565	\[ {} y^{\prime \prime }+y = 0 \]	✓	✓	✓

8566	\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

8567	\[ {} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]	✓	✓	✓

8568	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y = 0 \]	✓	✓	✓

8569	\[ {} 2 x y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

8570	\[ {} y^{\prime \prime }-x y^{\prime }-y = 0 \]	✓	✓	✓

8571	\[ {} \left (x -1\right ) y^{\prime \prime }+3 y = 0 \]	✓	✓	✓

8572	\[ {} x y-x^{2} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

8573	\[ {} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

8574	\[ {} y^{\prime \prime } \cos \left (x \right )+y = 0 \]	✓	✓	✓

8575	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✓

8576	\[ {} \left (x +2\right ) y^{\prime \prime }+3 y = 0 \]	✓	✓	✓

8577	\[ {} y^{\prime } \left (1+x \right ) = y \]	✓	✓	✓

8578	\[ {} y^{\prime } = -2 x y \]	✓	✓	✓

8579	\[ {} x y^{\prime }-3 y = k \]	✓	✓	✗

8580	\[ {} y^{\prime \prime }+y = 0 \]	✓	✓	✓

8581	\[ {} x y-y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

8582	\[ {} y^{\prime \prime }-y^{\prime }+x^{2} y = 0 \]	✓	✓	✓

8583	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]	✓	✓	✓

8584	\[ {} y^{\prime \prime }+\left (x^{2}+1\right ) y = 0 \]	✓	✓	✓

8585	\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]	✓	✓	✓

8586	\[ {} y^{\prime }+4 y = 1 \]	✓	✓	✓

8587	\[ {} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \]	✓	✓	✓

8588	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]	✓	✓	✓

8589	\[ {} \left (x -2\right ) y^{\prime } = x y \]	✓	✓	✓

8590	\[ {} \left (x -2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = 0 \]	✓	✓	✓

8591	\[ {} x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]	✓	✓	✓

8592	\[ {} y+x y^{\prime \prime } = 0 \]	✓	✓	✓

8593	\[ {} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \]	✓	✓	✓

8594	\[ {} x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

8595	\[ {} y^{\prime \prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

8596	\[ {} x y^{\prime \prime }+y^{\prime }+x y = 0 \]	✓	✓	✓

8597	\[ {} 2 x \left (x -1\right ) y^{\prime \prime }-y^{\prime } \left (1+x \right )+y = 0 \]	✓	✓	✓

8598	\[ {} x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \]	✓	✓	✓

8599	\[ {} x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0 \]	✓	✓	✓

8600	\[ {} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]	✓	✓	✓

8601	\[ {} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

8602	\[ {} 2 \left (1-x \right ) x y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

8603	\[ {} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

8604	\[ {} 4 x y^{\prime \prime }+y^{\prime }+8 y = 0 \]	✓	✓	✓

8605	\[ {} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

8606	\[ {} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]	✓	✓	✓

8607	\[ {} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]	✓	✓	✓

8608	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y = 0 \]	✓	✓	✓

8609	\[ {} x y^{\prime \prime }+y^{\prime }+\frac {y}{4} = 0 \]	✓	✓	✓

8610	\[ {} y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y = 0 \]	✓	✓	✓

8611	\[ {} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]	✓	✓	✓

8612	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {y \left (x^{2}-1\right )}{4} = 0 \]	✓	✓	✓

8613	\[ {} \left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x y \left (1+x \right ) = 0 \]	✓	✓	✓

8614	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y = 0 \]	✓	✓	✗

8615	\[ {} x y^{\prime \prime }+5 y^{\prime }+x y = 0 \]	✓	✓	✓

8616	\[ {} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y = 0 \]	✓	✓	✓

8617	\[ {} y^{\prime \prime }+x y = 0 \]	✓	✓	✓

8618	\[ {} 4 x y^{\prime \prime }+4 y^{\prime }+y = 0 \]	✓	✓	✓

8619	\[ {} x y^{\prime \prime }+y^{\prime }+36 y = 0 \]	✓	✓	✓

8620	\[ {} y^{\prime \prime }+k^{2} x^{2} y = 0 \]	✓	✓	✓

8621	\[ {} y^{\prime \prime }+k^{2} x^{4} y = 0 \]	✓	✓	✓

8622	\[ {} x y^{\prime \prime }-5 y^{\prime }+x y = 0 \]	✓	✓	✗

8623	\[ {} y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

8624	\[ {} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

8625	\[ {} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y = 0 \]	✓	✓	✗

8626	\[ {} 16 \left (1+x \right )^{2} y^{\prime \prime }+3 y = 0 \]	✓	✓	✗

8627	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y = 0 \]	✓	✓	✗

8628	\[ {} x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

4.7.11 Problems 1001 to 1100