2.3.63 Problems 6201 to 6300

Table 2.699: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6201	18470	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=4 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.475
6202	20504	\begin{align*} x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.475
6203	22480	\begin{align*} 2 y^{\prime \prime \prime \prime }&={\mathrm e}^{x}-{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.475
6204	23669	\begin{align*} \left (1-x \right ) y^{\prime \prime }-y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.475
6205	24259	\begin{align*} \left (x +a \right ) y^{\prime }&=b x \\ \end{align*}	✓	✓	✓	✓	0.475
6206	24601	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.475
6207	25240	\begin{align*} t y^{\prime \prime }-2 y^{\prime }+y t&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.475
6208	27654	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 x \,{\mathrm e}^{x}+{\mathrm e}^{x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.475
6209	651	\begin{align*} y^{\prime }&=2 x +1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.476
6210	2560	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.476
6211	8486	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.476
6212	10293	\begin{align*} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.476
6213	10626	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.476
6214	10674	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\ \end{align*}	✓	✓	✓	✗	0.476
6215	17617	\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.476
6216	20119	\begin{align*} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✗	0.476
6217	23830	\begin{align*} y^{\prime }&=\frac {1}{t^{2}-1} \\ \end{align*}	✓	✓	✓	✓	0.476
6218	1629	\begin{align*} y^{\prime }+y&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.477
6219	1872	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }-x y^{\prime }-3 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6220	3421	\begin{align*} y^{\prime }&=\frac {t}{t^{2}+4} \\ \end{align*}	✓	✓	✓	✓	0.477
6221	3988	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6222	7177	\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime \prime }+x y^{\prime }-n^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6223	7784	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.477
6224	8123	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.477
6225	8491	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6226	8561	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6227	8962	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6228	10069	\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.477
6229	10217	\begin{align*} x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477
6230	10302	\begin{align*} x \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.477
6231	10566	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.477
6232	10760	\begin{align*} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.477
6233	15982	\begin{align*} x^{\prime }&=-2 x-3 y \\ y^{\prime }&=3 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.477
6234	16073	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.477
6235	16164	\begin{align*} x y^{\prime }+\sqrt {x}&=2 \\ \end{align*}	✓	✓	✓	✓	0.477
6236	16704	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.477
6237	19512	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.477
6238	19661	\begin{align*} x^{\prime }&=\frac {1}{t^{2}+1} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.477
6239	21270	\begin{align*} x^{\prime \prime }+x^{\prime } t +x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.477
6240	21485	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.477
6241	21491	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.477
6242	21948	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.477
6243	21962	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.477
6244	23231	\begin{align*} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.477
6245	24140	\begin{align*} x +\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.477
6246	24460	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.477
6247	24673	\begin{align*} y^{\prime \prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.477
6248	26188	\begin{align*} y^{\prime }&=\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.477
6249	26969	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=21 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.477
6250	582	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=6 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.478
6251	3811	\begin{align*} x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.478
6252	7621	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -{\frac {17}{2}} \\ \end{align*}	✓	✓	✓	✓	0.478
6253	8855	\begin{align*} y^{\prime }&={\mathrm e}^{3 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.478
6254	9066	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.478
6255	11758	\begin{align*} y {y^{\prime }}^{2}-\left (-x +y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.478
6256	15189	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.478
6257	17013	\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=-4 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.478
6258	17900	\begin{align*} {\mathrm e}^{y^{\prime }}&=x \\ \end{align*}	✓	✓	✓	✓	0.478
6259	19552	\begin{align*} y^{\prime \prime }-y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.478
6260	22492	\begin{align*} y^{\prime \prime \prime \prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.478
6261	24021	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.478
6262	660	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.479
6263	3809	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.479
6264	8850	\begin{align*} x_{1}^{\prime }&=-x_{1}+3 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.479
6265	16831	\begin{align*} \left (x +1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.479
6266	23504	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.479
6267	24072	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.479
6268	26456	\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	0.479
6269	3110	\begin{align*} y^{\prime \prime }-4 y&=3 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.480
6270	3145	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.480
6271	3148	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.480
6272	4170	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=y_{1} \\ \end{align*}	✓	✓	✓	✓	0.480
6273	6705	\begin{align*} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.480
6274	8070	\begin{align*} y^{\prime }&=2 x^{2}+3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.480
6275	8492	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.480
6276	9444	\begin{align*} y^{\prime \prime }-y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.480
6277	12546	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.480
6278	14999	\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.480
6279	16020	\begin{align*} x^{\prime }&=-3 x+10 y \\ y^{\prime }&=-x+3 y \\ \end{align*}	✓	✓	✓	✓	0.480
6280	16158	\begin{align*} x^{2} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.480
6281	16633	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=4 x \,{\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✓	0.480
6282	19428	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.480
6283	20051	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{\frac {5 x}{2}} \\ \end{align*}	✓	✓	✓	✓	0.480
6284	20082	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.480
6285	21686	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.480
6286	23562	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.480
6287	23684	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.480
6288	24084	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.480
6289	24925	\begin{align*} y^{\prime }&=\frac {t +1}{t} \\ \end{align*}	✓	✓	✓	✓	0.480
6290	25085	\begin{align*} y^{\prime \prime }+4 y&=32 t \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.480
6291	444	\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 \(x=1\).	✓	✓	✓	✓	0.481
6292	1335	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.481
6293	3828	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.481
6294	4358	\begin{align*} 1+\cos \left (x \right ) y-\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.481
6295	9713	\begin{align*} {y^{\prime }}^{2} x^{2}+x y^{\prime }-y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.481
6296	12995	\begin{align*} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b&=0 \\ \end{align*}	✗	✗	✗	✗	0.481
6297	17397	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.481
6298	18900	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.481
6299	19744	\begin{align*} \sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\ \end{align*}	✓	✓	✓	✓	0.481
6300	20625	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.481