2.3.65 Problems 6401 to 6500

Table 2.703: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6401	24595	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.408
6402	24656	\begin{align*} y^{\prime \prime }+36 y&=\cos \left (6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.408
6403	25114	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.408
6404	25598	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{3} \\ \end{align*}	✓	✓	✓	✓	0.408
6405	25942	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.408
6406	2040	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.409
6407	5390	\begin{align*} {y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.409
6408	6148	\begin{align*} 4 y+2 \left (1-2 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.409
6409	8841	\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*}	✓	✓	✓	✓	0.409
6410	9521	\begin{align*} y^{\prime \prime }-y x&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.409
6411	10490	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.409
6412	10668	\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.409
6413	14934	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.409
6414	15980	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.409
6415	18675	\begin{align*} x^{\prime }&=a x+y \\ y^{\prime }&=-x+a y \\ \end{align*}	✓	✓	✓	✓	0.409
6416	18817	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.409
6417	21856	\begin{align*} x y^{2} {y^{\prime }}^{2}+\left (x^{3}+x y^{2}-y^{3}\right ) y^{\prime }+x^{3}-y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.409
6418	25267	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.409
6419	623	\begin{align*} x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.410
6420	836	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
6421	2236	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.410
6422	2619	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +\alpha \left (\alpha +1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.410
6423	3188	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.410
6424	3946	\begin{align*} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.410
6425	5391	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
6426	7987	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.410
6427	9031	\begin{align*} \cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
6428	9262	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.410
6429	9609	\begin{align*} y+y^{\prime }&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.410
6430	11688	\begin{align*} 2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
6431	14729	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.410
6432	15028	\begin{align*} {y^{\prime }}^{2}+x^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.410
6433	15261	\begin{align*} y^{\prime \prime }-3 y^{\prime }-7 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.410
6434	15432	\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.410
6435	18797	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.410
6436	19266	\begin{align*} y^{\prime } x&=2 x^{2}+1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.410
6437	26042	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }&=2 x^{3}-x \\ \end{align*}	✓	✓	✓	✓	0.410
6438	574	\begin{align*} x^{\prime \prime }+6 x^{\prime }+8 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
6439	1084	\begin{align*} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.411
6440	2034	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
6441	2057	\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
6442	2253	\begin{align*} y_{1}^{\prime }&=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-y_{1}+7 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.411
6443	2422	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +\alpha ^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.411
6444	3948	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
6445	4469	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.411
6446	6033	\begin{align*} -\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
6447	6366	\begin{align*} y^{\prime \prime }&=f \left (a x +b y, y^{\prime }\right ) \\ \end{align*}	✗	✗	✗	✗	0.411
6448	7755	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=8 \\ \end{align*}	✓	✓	✓	✓	0.411
6449	8098	\begin{align*} \left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
6450	9368	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
6451	9805	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.411
6452	10251	\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (2+x \right ) {\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.411
6453	10354	\begin{align*} y^{\prime } x +2 y x&=\sqrt {x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.411
6454	10520	\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
6455	11731	\begin{align*} x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
6456	12294	\begin{align*} y^{\prime \prime }-c \,x^{a} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
6457	14061	\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 y^{\prime } x -1&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
6458	14877	\begin{align*} y^{\prime }&=x -\frac {1}{3} x^{3} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.411
6459	15430	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.411
6460	15463	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (1\right ) &= 0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.411
6461	16028	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.411
6462	16183	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.411
6463	17895	\begin{align*} \cos \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
6464	19110	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
6465	19439	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.411
6466	21653	\begin{align*} y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-4 \left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.411
6467	21963	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.411
6468	22626	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.411
6469	23271	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
6470	23781	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.411
6471	24017	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\sin \left (x \right ) {\mathrm e}^{x} x \\ \end{align*}	✓	✓	✓	✓	0.411
6472	24651	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.411
6473	24898	\begin{align*} x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.411
6474	26124	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.411
6475	897	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.412
6476	1930	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
6477	2033	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
6478	3926	\begin{align*} x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.412
6479	8538	\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
6480	10584	\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
6481	11670	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
6482	13791	\begin{align*} x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (1+a \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
6483	14380	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.412
6484	14381	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.412
6485	16027	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=x-4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
6486	16056	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.412
6487	17742	\begin{align*} 15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
6488	18665	\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.412
6489	19025	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.412
6490	19892	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
6491	21122	\begin{align*} x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
6492	22690	\begin{align*} 4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.412
6493	22824	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
6494	23084	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1+x^{2}+{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.412
6495	23829	\begin{align*} y^{\prime }&=\cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.412
6496	24724	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.412
6497	25592	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.412
6498	449	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.413
6499	10684	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.413
6500	14276	\begin{align*} x+3 t x^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.413