2.3.64 Problems 6301 to 6400

Table 2.701: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6301	21935	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.481
6302	22737	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.481
6303	25134	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.481
6304	26754	\begin{align*} x^{\prime }&=t +2 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.481
6305	514	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.482
6306	1356	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u&=0 \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.482
6307	1843	\begin{align*} \left (3 x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.482
6308	2851	\begin{align*} x^{\prime }&=1-\sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.482
6309	3801	\begin{align*} y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.482
6310	7211	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.482
6311	7777	\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=50 x \\ \end{align*}	✓	✓	✓	✓	0.482
6312	8010	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.482
6313	12994	\begin{align*} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.482
6314	15194	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.482
6315	16067	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.482
6316	16939	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=8 x \\ \end{align*}	✓	✓	✓	✓	0.482
6317	16954	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.482
6318	21214	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.482
6319	23078	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=2 x^{3}+7 x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.482
6320	23985	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.482
6321	27664	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=7 x -3 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.482
6322	855	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.483
6323	1635	\begin{align*} y^{\prime }-2 y&=x y^{3} \\ y \left (0\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	0.483
6324	3121	\begin{align*} -2 y^{\prime \prime }+3 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.483
6325	3833	\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.483
6326	3927	\begin{align*} -2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.483
6327	4168	\begin{align*} y_{1}^{\prime }&=4 y_{2} \\ y_{2}^{\prime }&=4 y_{2}-y_{1} \\ \end{align*}	✓	✓	✓	✓	0.483
6328	10358	\begin{align*} x y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.483
6329	15202	\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.483
6330	16042	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-2 y \\ z^{\prime }&=-z \\ \end{align*}	✓	✓	✓	✓	0.483
6331	16618	\begin{align*} y^{\prime \prime }+9 y&=9 x^{4}-9 \\ \end{align*}	✓	✓	✓	✓	0.483
6332	16652	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.483
6333	17398	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.483
6334	21722	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.483
6335	23089	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.483
6336	23709	\begin{align*} x y^{\prime \prime }-2 y^{\prime }+y x&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= -2 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.483
6337	24119	\begin{align*} y^{\prime }-7 y&=-x^{4}+2 \\ y \left (0\right ) &= a \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.483
6338	24861	\begin{align*} {y^{\prime }}^{2} x^{2}-\left (x -y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.483
6339	25080	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.483
6340	27652	\begin{align*} y^{\prime \prime }-8 y^{\prime }+20 y&=5 x \,{\mathrm e}^{4 x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.483
6341	590	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.484
6342	1446	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.484
6343	1897	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.484
6344	2244	\begin{align*} y_{1}^{\prime }&=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.484
6345	3810	\begin{align*} x_{1}^{\prime }&=2 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.484
6346	3824	\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.484
6347	5803	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.484
6348	8482	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.484
6349	11670	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.484
6350	15995	\begin{align*} x^{\prime }&=-2 x-2 y \\ y^{\prime }&=-2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.484
6351	16077	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=4 \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.484
6352	16165	\begin{align*} \sqrt {x +4}\, y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.484
6353	17611	\begin{align*} 2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+t y^{\prime }-y&=-3 t^{2} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.484
6354	19171	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.484
6355	19194	\begin{align*} y^{\prime \prime }-2 y&=4 x^{2} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.484
6356	19671	\begin{align*} 3 x t^{2}-x t +\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.484
6357	19694	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.484
6358	20003	\begin{align*} y^{2} \left (1-{y^{\prime }}^{2}\right )&=b \\ \end{align*}	✓	✓	✓	✓	0.484
6359	24086	\begin{align*} \left (x^{3}+8\right ) y^{\prime \prime }+3 x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.484
6360	24712	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.484
6361	24796	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.484
6362	26110	\begin{align*} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.484
6363	27139	\begin{align*} x_{1}^{\prime }&=5 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.484
6364	27544	\begin{align*} 2 y^{\prime } \left (y^{\prime \prime }+2\right )&=x {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.484
6365	10514	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.485
6366	13157	\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.485
6367	15198	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.485
6368	19418	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.485
6369	21278	\begin{align*} s y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.485
6370	22316	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.485
6371	22600	\begin{align*} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime \prime }+24 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.485
6372	22706	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.485
6373	24537	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=27 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.485
6374	25815	\begin{align*} y^{\prime }&=\sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.485
6375	27671	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2^{x} \\ \end{align*}	✓	✓	✓	✓	0.485
6376	2240	\begin{align*} y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \\ \end{align*}	✓	✓	✓	✓	0.486
6377	3112	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.486
6378	7912	\begin{align*} 3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.486
6379	9667	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.486
6380	16507	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.486
6381	18344	\begin{align*} x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.486
6382	20075	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.486
6383	23674	\begin{align*} \left (x -1\right )^{4} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.486
6384	25116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.486
6385	589	\begin{align*} x^{\prime }&=-3 x+2 y \\ y^{\prime }&=-3 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.487
6386	658	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.487
6387	1308	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.487
6388	1864	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.487
6389	1906	\begin{align*} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -7 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.487
6390	3188	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.487
6391	6682	\begin{align*} 6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.487
6392	9231	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.487
6393	9317	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.487
6394	9443	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.487
6395	10384	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.487
6396	14366	\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.487
6397	16131	\begin{align*} y^{\prime \prime }+9 y&=2 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.487
6398	16524	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.487
6399	16605	\begin{align*} y^{\prime \prime }+9 y&=52 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.487
6400	17354	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.487