2.3.50 Problems 4901 to 5000

Table 2.631: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4901	10637	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
4902	10876	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
4903	10923	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
4904	12663	\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x}-\frac {a y}{x^{6}} \\ \end{align*}	✓	✓	✓	✓	0.261
4905	12817	\begin{align*} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+{\mathrm e}^{x} y-\frac {1}{x^{5}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
4906	15012	\begin{align*} x^{\prime }&=13 x \\ y^{\prime }&=13 y \\ \end{align*}	✓	✓	✓	✓	0.261
4907	16615	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \\ \end{align*}	✓	✓	✓	✓	0.261
4908	19857	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
4909	20116	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
4910	20915	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{2 t} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
4911	25603	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.261
4912	8552	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
4913	8817	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
4914	10293	\begin{align*} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
4915	10769	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
4916	10883	\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
4917	12706	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.262
4918	12865	\begin{align*} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.262
4919	17737	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
4920	23024	\begin{align*} z^{\prime \prime }-7 z^{\prime }-13 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
4921	23512	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.262
4922	23692	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
4923	23696	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
4924	24078	\begin{align*} 4 y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
4925	24904	\begin{align*} y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
4926	25806	\begin{align*} y^{\prime }&=\left (y-2\right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.262
4927	421	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
4928	1082	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
4929	2415	\begin{align*} y^{\prime \prime }-t^{3} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.263
4930	3571	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
4931	3692	\begin{align*} 2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
4932	4107	\begin{align*} y^{\prime }&=x +\frac {1}{x} \\ y \left (-2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.263
4933	5980	\begin{align*} \left (b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
4934	6478	\begin{align*} 2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.263
4935	6779	\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4936	7948	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
4937	8031	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4938	8174	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.263
4939	9349	\begin{align*} y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
4940	10604	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4941	10707	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4942	10879	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4943	10938	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4944	10967	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4945	11032	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4946	11064	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4947	12553	\begin{align*} -\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
4948	12778	\begin{align*} \sin \left (x \right )-y \cos \left (x \right )-3 \sin \left (x \right ) y^{\prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4949	14640	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }&=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \\ \end{align*}	✓	✓	✓	✓	0.263
4950	15417	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
4951	16053	\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.263
4952	16769	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.263
4953	16825	\begin{align*} y^{\prime }+\frac {y}{x -1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
4954	18374	\begin{align*} y^{\prime \prime }+y x&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
4955	20181	\begin{align*} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
4956	20886	\begin{align*} y^{\prime }&=y-x \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
4957	22501	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.263
4958	24614	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.263
4959	9	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.264
4960	438	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.264
4961	1527	\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.264
4962	1767	\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=\left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.264
4963	4127	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.264
4964	6307	\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\ \end{align*}	✗	✗	✗	✗	0.264
4965	6548	\begin{align*} 3 \left (1-y\right ) y y^{\prime \prime }&=2 \left (1-2 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.264
4966	6721	\begin{align*} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.264
4967	7572	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
4968	7823	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.264
4969	7826	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.264
4970	8569	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.264
4971	10294	\begin{align*} f \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
4972	10725	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
4973	10766	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
4974	10808	\begin{align*} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
4975	10837	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
4976	10855	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
4977	10871	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
4978	11070	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
4979	11205	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
4980	16006	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.264
4981	16054	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.264
4982	16428	\begin{align*} y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.264
4983	16703	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.264
4984	16850	\begin{align*} y^{\prime \prime }+y x&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.264
4985	16970	\begin{align*} y^{\prime \prime }-12 y^{\prime }+40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
4986	16980	\begin{align*} y^{\prime }&=\left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.264
4987	17416	\begin{align*} y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
4988	18938	\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.264
4989	20397	\begin{align*} \left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\ \end{align*}	✓	✓	✓	✓	0.264
4990	23772	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.264
4991	24085	\begin{align*} y^{\prime \prime }+3 x^{3} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.264
4992	24580	\begin{align*} y^{\prime \prime }+9 y&=15 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.264
4993	24632	\begin{align*} y^{\prime \prime }-9 y&=-72 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.264
4994	24711	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.264
4995	25175	\begin{align*} y_{1}^{\prime }-y_{1}&=-2 y_{2} \\ y_{2}^{\prime }-y_{2}&=2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.264
4996	25590	\begin{align*} y^{\prime \prime }+y&=t +{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.264
4997	10598	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.265
4998	19464	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.265
4999	19544	\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}	✓	✓	✓	✓	0.265
5000	24677	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.265