2.3.51 Problems 5001 to 5100

Table 2.645: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5001	624	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
5002	627	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
5003	1073	\begin{align*} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
5004	1418	\begin{align*} x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.332
5005	3195	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.332
5006	3711	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=4 x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	0.332
5007	3801	\begin{align*} y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.332
5008	6410	\begin{align*} y^{b}+x^{a} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.332
5009	8016	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
5010	8027	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }&=x +\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.332
5011	9114	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
5012	12601	\begin{align*} y^{\prime \prime }&=\frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}+\frac {y}{3 x^{2} \left (x -2\right )} \\ \end{align*}	✓	✓	✓	✗	0.332
5013	14339	\begin{align*} x^{\prime \prime }+t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
5014	16181	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.332
5015	17393	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
5016	17596	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=-\frac {1}{t^{2}}-\frac {2}{t} \\ \end{align*}	✓	✓	✓	✓	0.332
5017	18151	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.332
5018	18194	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.332
5019	18683	\begin{align*} i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }&=2 i-\frac {v}{2} \\ \end{align*}	✓	✓	✓	✓	0.332
5020	19514	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.332
5021	24904	\begin{align*} y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
5022	25062	\begin{align*} y^{\prime }+2 y&=3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
5023	25628	\begin{align*} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
5024	352	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.333
5025	658	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.333
5026	1083	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.333
5027	3710	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.333
5028	4492	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }-4 y&=50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.333
5029	6763	\begin{align*} 5 y^{\prime \prime \prime }+x y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
5030	8912	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.333
5031	10515	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
5032	18396	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
5033	18902	\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
5034	19563	\begin{align*} y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.333
5035	22250	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
5036	25109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.333
5037	25442	\begin{align*} y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.333
5038	25541	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
5039	840	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.334
5040	2371	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= v \\ \end{align*}	✓	✓	✓	✓	0.334
5041	3343	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.334
5042	8486	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.334
5043	8575	\begin{align*} y^{\prime }+4 y&=1 \\ y \left (0\right ) &= {\frac {5}{4}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.334
5044	15699	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.334
5045	20236	\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )+\cos \left (x \right ) x}{y \left (2 \ln \left (y\right )+1\right )} \\ \end{align*}	✓	✓	✓	✓	0.334
5046	20416	\begin{align*} y&=y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	0.334
5047	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*}	✓	✓	✓	✗	0.334
5048	22642	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
5049	23330	\begin{align*} 2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
5050	23335	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
5051	23487	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.334
5052	26248	\begin{align*} \tan \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.334
5053	292	\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*}	✓	✓	✓	✓	0.335
5054	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*}	✓	✓	✓	✓	0.335
5055	1288	\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*}	✓	✓	✓	✓	0.335
5056	2235	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
5057	3292	\begin{align*} {y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
5058	10507	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
5059	13200	\(\left [\begin {array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.335
5060	15693	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.335
5061	18259	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.335
5062	18697	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.335
5063	19500	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
5064	20186	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=n^{2} y \\ \end{align*}	✓	✓	✓	✓	0.335
5065	21714	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.335
5066	21724	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }+4 y&=0 \\ \end{align*} With initial conditions \begin{align*} z \left (0\right ) &= -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.335
5067	22194	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
5068	24710	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
5069	25981	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
5070	614	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 11 \\ x_{2} \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	0.336
5071	864	\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.336
5072	969	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.336
5073	1373	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5074	2200	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=-12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.336
5075	5871	\begin{align*} b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
5076	5910	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
5077	6135	\begin{align*} 2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
5078	7260	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
5079	8150	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5080	8498	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5081	8559	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5082	8573	\begin{align*} y^{\prime \prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5083	9717	\begin{align*} {y^{\prime }}^{2}-y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
5084	10075	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.336
5085	10587	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
5086	11670	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
5087	12633	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.336
5088	15260	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.336
5089	15471	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.336
5090	18208	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.336
5091	18696	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.336
5092	19579	\begin{align*} y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5093	19588	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
5094	19625	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
5095	20929	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.336
5096	20938	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=5 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.336
5097	21103	\begin{align*} x^{\prime }&=a y \\ y^{\prime }&=-a x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.336
5098	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.	✓	✓	✓	✓	0.336
5099	21771	\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✗	0.336
5100	21909	\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.	✓	✓	✓	✓	0.336