2.3.65 Problems 6401 to 6500

Table 2.673: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6401	4519	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.414
6402	5553	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
6403	5694	\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✗	0.414
6404	6402	\begin{align*} 2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.414
6405	6664	\begin{align*} \sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.414
6406	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*}	✓	✓	✓	✓	0.414
6407	11812	\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*}	✓	✓	✓	✓	0.414
6408	13190	\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.414
6409	16639	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
6410	16763	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.414
6411	18217	\begin{align*} y^{\prime \prime }+y&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
6412	18272	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.414
6413	18648	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.414
6414	18788	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.414
6415	21666	\begin{align*} y^{\prime \prime }&=y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.414
6416	22762	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.414
6417	24115	\begin{align*} y^{\prime }&=2 y \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.414
6418	24594	\begin{align*} y^{\prime \prime }-y&=\cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
6419	24630	\begin{align*} y^{\prime \prime }-4 y&=16 \,{\mathrm e}^{-2 x} x +8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.414
6420	24724	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
6421	24750	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \\ \end{align*}	✓	✓	✓	✓	0.414
6422	25244	\begin{align*} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.414
6423	3806	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.415
6424	5929	\begin{align*} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
6425	7976	\begin{align*} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
6426	9030	\begin{align*} 2 y^{3}+2+3 y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.415
6427	9605	\begin{align*} y^{\prime \prime }+y&=\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.415
6428	10399	\begin{align*} y^{\prime \prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.415
6429	11738	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
6430	16782	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.415
6431	18650	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=4 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.415
6432	19642	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.415
6433	23392	\begin{align*} 7 x^{4} y^{\prime \prime \prime \prime }-2 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.415
6434	1376	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.416
6435	1807	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=3 \,{\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.416
6436	3991	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.416
6437	7574	\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.416
6438	9313	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 y^{\prime \prime } x -8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.416
6439	9831	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.416
6440	10052	\begin{align*} 3 y y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.416
6441	16787	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.416
6442	16988	\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\ \end{align*}	✓	✓	✓	✓	0.416
6443	18094	\begin{align*} y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.416
6444	18662	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-5 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.416
6445	18955	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.416
6446	21516	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.416
6447	24552	\begin{align*} y^{\prime \prime }-y&=8 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.416
6448	25221	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t&=0 \\ \end{align*}	✓	✓	✓	✓	0.416
6449	513	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.417
6450	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.	✓	✓	✓	✓	0.417
6451	1093	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.417
6452	3503	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.417
6453	3923	\begin{align*} x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.417
6454	4510	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 \ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	0.417
6455	7729	\begin{align*} 2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.417
6456	8341	\begin{align*} y^{\prime }-\left (-1+y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.417
6457	9262	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.417
6458	9318	\begin{align*} y^{\prime \prime }-2 y^{\prime }-5 y&=x \\ \end{align*}	✓	✓	✓	✓	0.417
6459	18670	\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.417
6460	21543	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.417
6461	24013	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.417
6462	24892	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.417
6463	25566	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=5 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.417
6464	3136	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.418
6465	3290	\begin{align*} y^{2} {y^{\prime }}^{2}+y y^{\prime } x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
6466	4152	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.418
6467	8571	\begin{align*} y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.418
6468	8908	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=3 \,{\mathrm e}^{-x}+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.418
6469	10059	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.418
6470	13152	\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.418
6471	15322	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=f \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.418
6472	15405	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\sin \left (2 x \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.418
6473	15608	\begin{align*} y^{\prime }&=\frac {1}{x -1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.418
6474	18655	\begin{align*} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\ y^{\prime }&=\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.418
6475	19840	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.418
6476	2242	\begin{align*} y_{1}^{\prime }&=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.419
6477	3718	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.419
6478	4516	\begin{align*} y^{\prime \prime }+4 y&=8 \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.419
6479	8013	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.419
6480	8758	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.419
6481	8906	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.419
6482	12368	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.419
6483	15072	\begin{align*} y^{\prime \prime }+y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.419
6484	15766	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.419
6485	16766	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.419
6486	16954	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.419
6487	19425	\begin{align*} y^{\prime \prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.419
6488	23004	\begin{align*} 8 y^{\prime \prime }-10 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.419
6489	23012	\begin{align*} 2 y^{\prime \prime }-15 y^{\prime }+27 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.419
6490	25332	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.419
6491	25374	\begin{align*} y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.419
6492	486	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.420
6493	1415	\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.420
6494	2568	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.420
6495	2610	\begin{align*} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.420
6496	2615	\begin{align*} y^{\prime \prime }+t^{2} y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.420
6497	3159	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.420
6498	5789	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.420
6499	6119	\begin{align*} x \left (7+6 x \right ) y+x \left (1-x \right ) y^{\prime }+\left (-x^{2}-x +2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.420
6500	11005	\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.420