Problems 9401 to 9500

Table 6.189: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

9401	\[ {} x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0 \]	✓	✓	✓

9402	\[ {} x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0 \]	✓	✓	✗

9403	\[ {} x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0 \]	✓	✗	✗

9404	\[ {} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0 \]	✓	✓	✗

9405	\[ {} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0 \]	✓	✓	✓

9406	\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x y = 0 \]	✓	✓	✓

9407	\[ {} x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0 \]	✓	✓	✗

9408	\[ {} 4 x y^{\prime \prime }+3 y^{\prime }+y = 0 \]	✓	✓	✓

9409	\[ {} 2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0 \]	✓	✓	✓

9410	\[ {} 2 x y^{\prime \prime }+y^{\prime } \left (1+x \right )+3 y = 0 \]	✓	✓	✓

9411	\[ {} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y = 0 \]	✓	✓	✓

9412	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \]	✓	✓	✓

9413	\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0 \]	✓	✗	✗

9414	\[ {} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]	✓	✗	✗

9415	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4+4 x \right ) y = 0 \]	✓	✓	✓

9416	\[ {} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \]	✓	✓	✓

9417	\[ {} x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]	✓	✓	✓

9418	\[ {} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

9419	\[ {} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]	✓	✓	✓

9420	\[ {} \left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0 \]	✓	✓	✗

9421	\[ {} 3 \left (1+x \right )^{2} y^{\prime \prime }-y^{\prime } \left (1+x \right )-y = 0 \]	✓	✓	✗

9422	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0 \]	✓	✓	✓

9423	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

9424	\[ {} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

9425	\[ {} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

9426	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0 \]	✓	✓	✓

9427	\[ {} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

9428	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \]	✓	✓	✓

9429	\[ {} \left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0 \]	✓	✓	✗

9430	\[ {} y^{\prime \prime }+2 x y = x^{2} \]	✓	✓	✗

9431	\[ {} y^{\prime \prime }-x y^{\prime }+y = x \]	✓	✓	✗

9432	\[ {} y^{\prime \prime }+y^{\prime }+y = x^{3}-x \]	✓	✓	✗

9433	\[ {} 2 y^{\prime \prime }+x y^{\prime }+y = 0 \]	✓	✓	✓

9434	\[ {} \left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0 \]	✓	✓	✓

9435	\[ {} y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

9436	\[ {} y^{\prime \prime }-y^{\prime } \left (1+x \right )-x y = 0 \]	✓	✓	✓

9437	\[ {} \left (x -1\right ) y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 0 \]	✓	✓	✓

9438	\[ {} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (x +2\right ) y = 0 \]	✓	✓	✗

9439	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0 \]	✓	✓	✗

9440	\[ {} x y^{\prime \prime }-4 y^{\prime }+x y = 0 \]	✓	✓	✓

9441	\[ {} 4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0 \]	✓	✓	✗

9442	\[ {} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

9443	\[ {} x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

9444	\[ {} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0 \]	✓	✓	✗

9445	\[ {} x y^{\prime \prime }+y^{\prime } \left (1+x \right )+y = 0 \]	✓	✓	✓

9446	\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0 \]	✓	✓	✗

9447	\[ {} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✗

9448	\[ {} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0 \]	✓	✓	✗

9449	\[ {} x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✗

9450	\[ {} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \]	✓	✓	✓

9451	\[ {} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y = 0 \]	✓	✓	✗

9452	\[ {} p \left (p +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

9453	\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \]	✓	✓	✓

9454	\[ {} y^{\prime \prime }+y^{\prime }-6 y = t \]	✓	✓	✓

9455	\[ {} y^{\prime \prime }-y = t^{2} \]	✓	✓	✓

9456	\[ {} L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right ) \]	✓	✓	✗

9457	\[ {} L i^{\prime }+R i = E_{0} \delta \left (t \right ) \]	✓	✓	✓

9458	\[ {} L i^{\prime }+R i = E_{0} \sin \left (\omega t \right ) \]	✓	✓	✓

9459	\[ {} y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]	✓	✓	✓

9460	\[ {} y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t} \]	✓	✓	✓

9461	\[ {} y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \]	✓	✓	✓

9462	\[ {} y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]	✓	✓	✓

9463	\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]	✓	✓	✓

9464	\[ {} y^{\prime \prime }+3 y^{\prime }+3 y = 2 \]	✓	✓	✓

9465	\[ {} y^{\prime \prime }+y^{\prime }+2 y = t \]	✓	✓	✓

9466	\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \]	✓	✓	✓

9467	\[ {} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]	✓	✗	✗

9468	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]	✓	✓	✓

9469	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]	✓	✓	✓

9470	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )] \]	✓	✓	✓

9471	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+t -1, y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )-5 t -2] \]	✓	✓	✓

9472	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]	✓	✓	✓

9473	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )] \]	✓	✓	✓

9474	\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )] \]	✓	✓	✓

9475	\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )] \]	✓	✓	✓

9476	\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]	✓	✓	✓

9477	\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )] \]	✓	✓	✓

9478	\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )] \]	✓	✓	✓

9479	\[ {} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]	✓	✓	✓

9480	\[ {} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )] \]	✓	✓	✓

9481	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )] \]	✓	✓	✓

9482	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 t +2, y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )-8 t -8] \]	✓	✓	✓

9483	\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )] \]	✓	✓	✓

9484	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )] \]	✓	✓	✓

9485	\[ {} \left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\sqrt {2}\, y \left (t \right ), y^{\prime }\left (t \right ) = \sqrt {2}\, x \left (t \right )-2 y \left (t \right )\right ] \]	✓	✓	✓

9486	\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )] \]	✓	✓	✓

9487	\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )] \]	✓	✓	✓

9488	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]	✓	✓	✓

9489	\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )] \]	✓	✓	✓

9490	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )] \]	✓	✓	✓

9491	\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )] \]	✓	✓	✓

9492	\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+z \left (t \right )] \]	✓	✓	✗

9493	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-4 t +1, y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )+3 t +4] \]	✓	✓	✓

9494	\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+t -2] \]	✓	✓	✓

9495	\[ {} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = -x \left (t \right )-5 y \left (t \right )+t +1] \]	✓	✓	✓

9496	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]	✗	✗	✗

9497	\[ {} [x^{\prime }\left (t \right ) = 1+t y \left (t \right ), y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )] \]	✗	✗	✗

9498	\[ {} y^{\prime } = -x +y^{2} \]	✓	✓	✓

9499	\[ {} y^{\prime } = -x +y^{2} \]	✓	✓	✗

9500	\[ {} y^{\prime }-2 y = x^{2} \]	✓	✓	✓

6.95 Problems 9401 to 9500