2.3.51 Problems 5001 to 5100

Table 2.675: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5001	18685	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*}	✓	✓	✓	✓	0.342
5002	20582	\begin{align*} n \,x^{3} y^{\prime \prime \prime }&=y-y^{\prime } x \\ \end{align*}	✓	✓	✓	✗	0.342
5003	22643	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5004	22737	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.342
5005	23386	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.342
5006	25910	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5007	26486	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5008	26792	\begin{align*} y^{\prime \prime \prime }+\alpha y^{\prime \prime }+\beta y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5009	27686	\begin{align*} y^{\prime \prime }-2 y&=2 x \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.342
5010	1363	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.343
5011	1880	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.343
5012	2595	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{t} t^{2} \\ \end{align*}	✓	✓	✓	✓	0.343
5013	3940	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.343
5014	6240	\begin{align*} -2 y+y^{\prime } x +x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
5015	6509	\begin{align*} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
5016	8044	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (9 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
5017	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*}	✓	✓	✓	✓	0.343
5018	10603	\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*}	✓	✓	✓	✗	0.343
5019	10614	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
5020	12785	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
5021	14407	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=-2 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.343
5022	14412	\begin{align*} x^{\prime }&=x-3 y \\ y^{\prime }&=3 x+7 y \\ \end{align*}	✓	✓	✓	✓	0.343
5023	16540	\begin{align*} y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -28 \\ y^{\prime \prime }\left (0\right ) &= -102 \\ y^{\prime \prime \prime }\left (0\right ) &= 622 \\ \end{align*}	✓	✓	✓	✓	0.343
5024	21572	\begin{align*} y^{\prime \prime }-y&=2 x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.343
5025	22098	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
5026	23330	\begin{align*} 2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
5027	26355	\begin{align*} x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\ \end{align*}	✓	✓	✓	✓	0.343
5028	27131	\(\left [\begin {array}{cc} 0 & 2 i \\ 2 i & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.343
5029	2368	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.344
5030	5886	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5031	6410	\begin{align*} y^{b}+x^{a} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.344
5032	9259	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.344
5033	10086	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	0.344
5034	11727	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5035	25628	\begin{align*} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.344
5036	151	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.345
5037	446	\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.345
5038	1009	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.345
5039	1374	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
5040	1886	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
5041	2593	\begin{align*} y^{\prime \prime }+3 y&=t^{3}-1 \\ \end{align*}	✓	✓	✓	✓	0.345
5042	6505	\begin{align*} y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.345
5043	7074	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.345
5044	8570	\begin{align*} y x -y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
5045	9453	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.345
5046	10678	\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
5047	13688	\begin{align*} y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.345
5048	14378	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.345
5049	14822	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.345
5050	16464	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.345
5051	18686	\begin{align*} x^{\prime }&=-\frac {3 x}{2}+y \\ y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\ \end{align*}	✓	✓	✓	✓	0.345
5052	18761	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
5053	21210	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.345
5054	21526	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.345
5055	21774	\begin{align*} y {y^{\prime }}^{2}-\left (y x +x +y^{2}\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✗	✗	0.345
5056	23806	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.345
5057	23824	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.345
5058	23825	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.345
5059	24811	\begin{align*} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.345
5060	26247	\begin{align*} \tan \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.345
5061	27678	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.345
5062	447	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ y \left (-3\right ) &= 0 \\ y^{\prime }\left (-3\right ) &= 2 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.346
5063	2404	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=t \,{\mathrm e}^{3 t}+1 \\ \end{align*}	✓	✓	✓	✓	0.346
5064	3421	\begin{align*} y^{\prime }&=\frac {t}{t^{2}+4} \\ \end{align*}	✓	✓	✓	✓	0.346
5065	6773	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
5066	8129	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.346
5067	10239	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
5068	10693	\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
5069	11021	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
5070	18283	\begin{align*} y^{\prime \prime }-y&=-2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.346
5071	19241	\begin{align*} y^{\prime }&={\mathrm e}^{3 x}-x \\ \end{align*}	✓	✓	✓	✓	0.346
5072	21146	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.346
5073	22644	\begin{align*} 4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
5074	27593	\begin{align*} y \left (2 y^{\prime \prime } x +y^{\prime }\right )&=x {y^{\prime }}^{2}+1 \\ \end{align*}	✗	✓	✓	✗	0.346
5075	2782	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.347
5076	3186	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.347
5077	4383	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.347
5078	5477	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5079	8340	\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5080	8941	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.347
5081	9066	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.347
5082	9171	\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5083	10465	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.347
5084	10605	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.347
5085	10694	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.347
5086	15414	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5087	16558	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5088	16727	\begin{align*} y^{\prime \prime }+y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5089	21224	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.347
5090	21748	\begin{align*} y^{\prime }&=y-3 z \\ z^{\prime }&=2 y-4 z \\ \end{align*}	✓	✓	✓	✓	0.347
5091	23030	\begin{align*} z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
5092	25174	\begin{align*} y_{1}^{\prime }&=-y_{2} \\ y_{2}^{\prime }-2 y_{2}&=y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.347
5093	27577	\begin{align*} x y y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+y\right ) \\ \end{align*}	✗	✓	✓	✗	0.347
5094	27647	\begin{align*} y^{\prime \prime }+y&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.347
5095	358	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (3 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.348
5096	843	\begin{align*} y^{\prime \prime }+2 y&=6 x \\ \end{align*}	✓	✓	✓	✓	0.348
5097	1379	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.348
5098	3338	\begin{align*} y^{\prime }&=\ln \left (y x \right ) \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.348
5099	4134	\begin{align*} y^{\prime \prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.348
5100	4135	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.348