2.3.50 Problems 4901 to 5000

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4901	23044	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.388
4902	23690	\begin{align*} y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.388
4903	23794	\begin{align*} x^{\prime }&=4 x-6 y \\ y^{\prime }&=8 x-10 y \\ \end{align*}	✓	✓	✓	✓	0.388
4904	24047	\begin{align*} y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.388
4905	24440	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.388
4906	26133	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.388
4907	27191	\begin{align*} x_{1}^{\prime }&=9 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.388
4908	1259	\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.389
4909	1862	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
4910	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*}	✓	✓	✓	✓	0.389
4911	6657	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.389
4912	16823	\begin{align*} \left (x -3\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
4913	16985	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.389
4914	1786	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=4 x^{4} \\ y \left (-1\right ) &= 7 \\ y^{\prime }\left (-1\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.390
4915	2682	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=1+{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.390
4916	7078	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.390
4917	9487	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.390
4918	14354	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.390
4919	18775	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.390
4920	23600	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.390
4921	25911	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.390
4922	27645	\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.390
4923	1087	\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 ) &= 1 \\ y^{\prime }\left (-3\right ) &= 0 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.391
4924	1744	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.391
4925	1887	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.391
4926	2366	\begin{align*} 3 y^{\prime \prime }+6 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.391
4927	2613	\begin{align*} y^{\prime \prime }-t^{3} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.391
4928	3925	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.391
4929	4517	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.391
4930	8606	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.391
4931	10771	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.391
4932	16495	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.391
4933	19435	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.391
4934	20884	\begin{align*} y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.391
4935	23067	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.391
4936	25061	\begin{align*} y^{\prime }+a y&={\mathrm e}^{-a t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.391
4937	26677	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.391
4938	27532	\begin{align*} y^{\prime \prime } \left (1+{\mathrm e}^{x}\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.391
4939	893	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.392
4940	2558	\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.392
4941	4515	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.392
4942	6736	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.392
4943	7590	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.392
4944	7987	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.392
4945	8128	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.392
4946	11069	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.392
4947	19439	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.392
4948	20888	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.392
4949	23033	\begin{align*} y^{\prime \prime }-3 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.392
4950	23787	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.392
4951	24439	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.392
4952	27071	\begin{align*} y^{\prime \prime }+x y^{\prime }&=1-{\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.392
4953	2378	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.393
4954	7277	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.393
4955	8071	\begin{align*} \left (x +1\right ) y^{\prime }&=x^{2}-2 x +y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.393
4956	10352	\begin{align*} x y^{\prime }+y&=2 x^{4}+x^{3}+x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.393
4957	10980	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.393
4958	11034	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.393
4959	11727	\begin{align*} {y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.393
4960	13998	\begin{align*} y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.393
4961	20343	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.393
4962	27190	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.393
4963	405	\begin{align*} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.394
4964	978	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.394
4965	3617	\begin{align*} y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.394
4966	6615	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.394
4967	16413	\begin{align*} \left (-3+y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.394
4968	16429	\begin{align*} y^{\prime \prime }&=-2 {y^{\prime }}^{2} x \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.394
4969	19478	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.394
4970	21914	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= {\frac {3}{2}} \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.394
4971	23831	\begin{align*} y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.394
4972	24922	\begin{align*} y^{\prime }&=t +3 \\ \end{align*}	✓	✓	✓	✓	0.394
4973	26941	\begin{align*} y^{\prime \prime }+3 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.394
4974	27713	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.394
4975	1263	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.395
4976	1368	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.395
4977	1460	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.395
4978	2387	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
4979	7719	\begin{align*} x y^{\prime }-y&=x^{3} \cos \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.395
4980	8102	\begin{align*} y^{\prime \prime }&=\left (x -1\right ) y \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.395
4981	9030	\begin{align*} 2 y^{3}+2+3 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
4982	10986	\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*}	✓	✓	✓	✗	0.395
4983	11729	\begin{align*} {y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
4984	16047	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
4985	18131	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
4986	19993	\begin{align*} y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	0.395
4987	21204	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.395
4988	22242	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.395
4989	26343	\begin{align*} {y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
4990	27650	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x}+x \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.395
4991	3099	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
4992	7583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
4993	9467	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.396
4994	10303	\begin{align*} x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
4995	16163	\begin{align*} y^{\prime }&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.396
4996	19782	\begin{align*} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \\ \end{align*}	✗	✗	✗	✗	0.396
4997	23358	\begin{align*} 5 y^{\prime \prime }+10 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
4998	23613	\begin{align*} x^{\prime }&=4 x+3 y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.396
4999	24865	\begin{align*} {y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
5000	409	\begin{align*} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.397