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	11063	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4902	11129	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4903	13676	\begin{align*} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4904	13816	\begin{align*} n \left (n +2\right ) y-3 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4905	14384	\begin{align*} x^{\prime }&=-2 x \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.338
4906	15014	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.338
4907	16461	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.338
4908	17648	\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.338
4909	18379	\begin{align*} y^{\prime }-2 y x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4910	18692	\begin{align*} x^{\prime }&=2 x+\frac {3 y}{2} \\ y^{\prime }&=-\frac {3 x}{2}-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.338
4911	19022	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }&=x_{1}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.338
4912	20840	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4913	20866	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4914	22164	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.338
4915	27648	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.338
4916	456	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4917	581	\begin{align*} x^{\prime }&=8 y \\ y^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.339
4918	1073	\begin{align*} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4919	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 \(x=1\).	✓	✓	✓	✓	0.339
4920	1459	\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 ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.339
4921	3146	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.339
4922	3324	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.339
4923	3936	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4924	5366	\begin{align*} {y^{\prime }}^{2}&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.339
4925	5694	\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✗	0.339
4926	6040	\begin{align*} \left (3 a x +5\right ) y-x \left (a x +5\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4927	6763	\begin{align*} 5 y^{\prime \prime \prime }+x y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4928	8911	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.339
4929	9599	\begin{align*} -y+y^{\prime }&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4930	9819	\begin{align*} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4931	10633	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4932	10648	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4933	10650	\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*}	✓	✓	✓	✗	0.339
4934	10695	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4935	10718	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4936	11027	\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4937	14321	\begin{align*} x^{\prime \prime }&=-\frac {x}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.339
4938	16488	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4939	16804	\begin{align*} y^{\prime \prime }&=\delta \left (t -1\right )-\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4940	17562	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.339
4941	18081	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.339
4942	19593	\begin{align*} x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.339
4943	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.	✓	✓	✓	✓	0.339
4944	21586	\begin{align*} y^{\prime \prime }-y&=x^{2}-x +1 \\ \end{align*}	✓	✓	✓	✓	0.339
4945	22783	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.339
4946	23314	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4947	24473	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4948	24546	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \cos \left (x \right )+4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.339
4949	24676	\begin{align*} 4 y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.339
4950	27683	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.339
4951	621	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.340
4952	9218	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4953	9455	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.340
4954	10518	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.340
4955	13687	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.340
4956	18387	\begin{align*} \left (x +1\right ) y^{\prime }-n y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4957	19866	\begin{align*} 4 y^{\prime }+5 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=-\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.340
4958	21116	\begin{align*} x^{\prime \prime }+4 x^{\prime }+k x&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4959	21519	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=2 x^{3}+5 x^{2}-7 x +2 \\ \end{align*}	✓	✓	✓	✓	0.340
4960	21800	\begin{align*} x^{3} y^{\prime }-x^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	0.340
4961	22249	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.340
4962	23392	\begin{align*} 7 x^{4} y^{\prime \prime \prime \prime }-2 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4963	24542	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.340
4964	25670	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.340
4965	2702	\begin{align*} x^{\prime }&=x-3 y \\ y^{\prime }&=-2 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.341
4966	7593	\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4967	8962	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4968	9225	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4969	10689	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4970	10951	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4971	11065	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4972	13881	\begin{align*} \left (x^{2}-1\right )^{2} y^{\prime \prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4973	21530	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.341
4974	21941	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{x}}{x^{3}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.341
4975	23630	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.341
4976	24012	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.341
4977	25095	\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4978	25116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.341
4979	25997	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.341
4980	1744	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4981	2625	\begin{align*} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.342
4982	3189	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \\ \end{align*}	✓	✓	✓	✓	0.342
4983	8005	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.342
4984	8135	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.342
4985	8578	\begin{align*} \left (x -2\right ) y^{\prime }&=y x \\ y \left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.342
4986	9604	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
4987	9620	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=1+t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
4988	10402	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.342
4989	10724	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.342
4990	11295	\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.342
4991	12641	\begin{align*} y^{\prime \prime }&=-\frac {2 \left (x^{2}-1\right ) y^{\prime }}{x \left (x -1\right )^{2}}-\frac {\left (-2 x^{2}+2 x +2\right ) y}{x^{2} \left (x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.342
4992	13773	\begin{align*} x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-n \left (n +1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4993	14582	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4994	15026	\begin{align*} {y^{\prime }}^{2}&=9 y^{4} \\ \end{align*}	✓	✓	✓	✓	0.342
4995	16052	\(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.342
4996	16581	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4997	17370	\begin{align*} t^{2} y^{\prime \prime }+6 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4998	17561	\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4999	17587	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.342
5000	17829	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.342