2.3.65 Problems 6401 to 6500

Table 2.661: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6401	24838	\begin{align*} 9 y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
6402	624	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.330
6403	1067	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
6404	1318	\begin{align*} y^{\prime \prime }-y^{\prime }+\frac {y}{4}&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	0.330
6405	1333	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.330
6406	1459	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.330
6407	2801	\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.330
6408	5786	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} x \\ \end{align*}	✓	✓	✓	✓	0.330
6409	5957	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
6410	7770	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.330
6411	8396	\begin{align*} y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.330
6412	8559	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
6413	15303	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
6414	16074	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.330
6415	18648	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.330
6416	22129	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.330
6417	22729	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.330
6418	22730	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 x}+x \\ \end{align*}	✓	✓	✓	✓	0.330
6419	22763	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.330
6420	23445	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
6421	25595	\begin{align*} y^{\prime \prime }+3 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.330
6422	1360	\begin{align*} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5}&=\cos \left (t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.331
6423	1862	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.331
6424	2783	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.331
6425	5808	\begin{align*} \left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
6426	7656	\begin{align*} y^{\prime }-y x&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.331
6427	7756	\begin{align*} y^{\prime \prime }-4 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.331
6428	8044	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (9 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
6429	15513	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.331
6430	18693	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.331
6431	20179	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
6432	22018	\begin{align*} y^{\prime }&=\frac {2 y x}{y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.331
6433	24048	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=x^{2}-4 \cos \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
6434	24570	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }-3 y&=-9 x^{2}-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.331
6435	25229	\begin{align*} t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
6436	368	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.332
6437	869	\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.332
6438	870	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=3 x +4 \\ \end{align*}	✓	✓	✓	✓	0.332
6439	1263	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
6440	1450	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
6441	2622	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.332
6442	3403	\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.332
6443	3833	\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
6444	4649	\begin{align*} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+y f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
6445	6324	\begin{align*} y^{\prime \prime }&=\operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	0.332
6446	6531	\begin{align*} 4 f \left (x \right ) y y^{\prime \prime }&=4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.332
6447	7597	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\ y \left (-1\right ) &= 3 \\ y^{\prime }\left (-1\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.332
6448	8204	\begin{align*} y^{\prime }&=5-y \\ \end{align*}	✓	✓	✓	✓	0.332
6449	8807	\begin{align*} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t}&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
6450	8845	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
6451	8851	\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.332
6452	8901	\begin{align*} y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
6453	10402	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
6454	10569	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
6455	14875	\begin{align*} T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
6456	15514	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.332
6457	16429	\begin{align*} y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.332
6458	16937	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.332
6459	19020	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
6460	19057	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.332
6461	20148	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
6462	22689	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+15 x \\ \end{align*}	✓	✓	✓	✓	0.332
6463	24018	\begin{align*} y^{\prime \prime \prime }+3 k y^{\prime \prime }+3 k^{2} y^{\prime }+k^{3} y&={\mathrm e}^{-k x} f^{\prime \prime \prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
6464	24560	\begin{align*} 4 y+y^{\prime \prime }&=4 \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.332
6465	24728	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
6466	24810	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
6467	25329	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.332
6468	627	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.333
6469	893	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.333
6470	3099	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
6471	3715	\begin{align*} y^{\prime \prime }+y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.333
6472	3828	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.333
6473	6104	\begin{align*} 6 y+\left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
6474	7652	\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
6475	8561	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
6476	9843	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
6477	10222	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.333
6478	10446	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
6479	14572	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.333
6480	14928	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.333
6481	14932	\begin{align*} x^{\prime \prime }-4 x&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.333
6482	14957	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.333
6483	16114	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.333
6484	18383	\begin{align*} y^{\prime \prime }&=x^{2} y-y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
6485	18656	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.333
6486	21206	\begin{align*} x^{\prime }&=a x+y \\ y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	0.333
6487	22236	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
6488	22713	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.333
6489	22740	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.333
6490	22891	\begin{align*} x^{\prime }-2 y^{\prime }&={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }&=\sqrt {t} \\ \end{align*}	✓	✓	✓	✓	0.333
6491	24086	\begin{align*} \left (x^{3}+8\right ) y^{\prime \prime }+3 x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
6492	24714	\begin{align*} 4 y+y^{\prime \prime }&=2 x -8 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.333
6493	25306	\begin{align*} y^{\prime }+2 y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
6494	6277	\begin{align*} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (-x +2\right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
6495	10076	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.334
6496	12905	\begin{align*} 2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.334
6497	15700	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.334
6498	16161	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
6499	18691	\begin{align*} x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.334
6500	21537	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 x^{2}+4 \sin \left (x \right )-2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.334