Problems 1301 to 1400

Table 4.1037: Second or higher order ODE with non-constant coeﬃcients


#	ODE	Mathematica	Maple	Sympy

9573	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]	✓	✓	✗

9574	\[ {} 3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \]	✓	✓	✗

9575	\[ {} 5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]	✓	✓	✗

9576	\[ {} y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]	✓	✓	✗

9577	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]	✓	✓	✗

9578	\[ {} y^{\prime \prime }+x y^{\prime }-2 y = 0 \]	✓	✓	✗

9579	\[ {} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]	✓	✓	✗

9580	\[ {} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]	✓	✓	✗

9581	\[ {} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \]	✓	✓	✓

9582	\[ {} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0 \]	✓	✓	✓

9583	\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✗

9584	\[ {} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]	✓	✓	✓

9585	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

9586	\[ {} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0 \]	✓	✓	✓

9587	\[ {} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

9588	\[ {} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]	✓	✓	✓

9589	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

9590	\[ {} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

9591	\[ {} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]	✓	✓	✓

9592	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✗

9593	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]	✓	✓	✗

9594	\[ {} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]	✓	✓	✗

9595	\[ {} 2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \]	✓	✓	✗

9596	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✗

9597	\[ {} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]	✓	✓	✗

9598	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✗

9599	\[ {} \left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✗

9600	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]	✓	✓	✓

9601	\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✗

9602	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

9603	\[ {} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \]	✓	✓	✗

9604	\[ {} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \]	✓	✓	✗

9605	\[ {} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]	✓	✓	✗

9606	\[ {} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]	✓	✓	✗

9607	\[ {} x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = 0 \]	✓	✓	✗

9608	\[ {} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = 0 \]	✓	✓	✗

9609	\[ {} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0 \]	✓	✓	✗

9610	\[ {} 2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0 \]	✓	✓	✗

9611	\[ {} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \]	✓	✓	✗

9612	\[ {} 4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 0 \]	✓	✓	✗

9613	\[ {} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y = 0 \]	✓	✓	✗

9614	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]	✓	✓	✓

9615	\[ {} x y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0 \]	✓	✓	✗

9616	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

9617	\[ {} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \]	✓	✓	✗

9618	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]	✓	✓	✓

9619	\[ {} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0 \]	✓	✓	✗

9620	\[ {} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \]	✓	✓	✗

9621	\[ {} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \]	✓	✓	✗

9622	\[ {} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]	✓	✓	✗

9623	\[ {} \left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = 0 \]	✓	✓	✓

9624	\[ {} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]	✓	✓	✗

9625	\[ {} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]	✓	✓	✗

9626	\[ {} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \]	✓	✓	✗

9627	\[ {} x y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0 \]	✓	✓	✗

9628	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

9629	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]	✓	✓	✓

9630	\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0 \]	✓	✓	✓

9631	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

9632	\[ {} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \]	✓	✓	✗

9633	\[ {} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0 \]	✓	✓	✗

9634	\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]	✓	✓	✓

9635	\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✗

9636	\[ {} 4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 0 \]	✓	✓	✗

9637	\[ {} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]	✓	✓	✗

9638	\[ {} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \]	✓	✓	✗

9639	\[ {} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \]	✓	✓	✗

9640	\[ {} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \]	✓	✓	✗

9641	\[ {} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \]	✓	✓	✗

9642	\[ {} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \]	✓	✓	✗

9643	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \]	✓	✓	✗

9644	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]	✓	✓	✗

9645	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]	✓	✓	✗

9646	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]	✓	✓	✗

9647	\[ {} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]	✓	✓	✗

9648	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \]	✓	✓	✗

9649	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]	✓	✓	✗

9650	\[ {} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✗

9651	\[ {} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0 \]	✓	✓	✗

9652	\[ {} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \]	✓	✓	✗

9653	\[ {} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]	✓	✓	✗

9654	\[ {} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \]	✓	✓	✓

9655	\[ {} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]	✓	✓	✗

9656	\[ {} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]	✗	✓	✓

9657	\[ {} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]	✓	✓	✗

9658	\[ {} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]	✗	✓	✗

9659	\[ {} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]	✓	✓	✓

9660	\[ {} \left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]	✓	✓	✗

9661	\[ {} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]	✓	✓	✗

9662	\[ {} \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \]	✓	✓	✗

9663	\[ {} \left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0 \]	✓	✓	✗

9664	\[ {} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \]	✓	✓	✗

9665	\[ {} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \]	✓	✓	✗

9666	\[ {} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \]	✓	✓	✗

9667	\[ {} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \]	✓	✓	✗

9668	\[ {} y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]	✓	✓	✗

9669	\[ {} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \]	✓	✓	✗

9670	\[ {} y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \]	✓	✓	✗

9671	\[ {} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]	✓	✓	✗

9672	\[ {} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]	✓	✓	✗

4.24.14 Problems 1301 to 1400