2.3.48 Problems 4701 to 4800

Table 2.627: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4701	659	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.253
4702	1050	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
4703	2567	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4704	5393	\begin{align*} {y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4705	5920	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
4706	8606	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
4707	10296	\begin{align*} y^{\prime } x&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.253
4708	10521	\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
4709	10672	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4710	10692	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
4711	10886	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
4712	10959	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
4713	12614	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}+\frac {y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.253
4714	12705	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (x -1\right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.253
4715	13146	\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.253
4716	14581	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4717	15715	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.253
4718	15809	\begin{align*} y^{\prime }&=t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.253
4719	16986	\begin{align*} y^{\prime }&=\frac {-2 x -10}{\left (2+x \right ) \left (x -4\right )} \\ \end{align*}	✓	✓	✓	✓	0.253
4720	17027	\begin{align*} y^{\prime }&=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	0.253
4721	17384	\begin{align*} y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4722	21569	\begin{align*} y^{\prime \prime }-2 s y^{\prime }-2 y&=0 \\ \end{align*}	✗	✓	✓	✓	0.253
4723	23593	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.253
4724	25100	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4725	25237	\begin{align*} t y^{\prime \prime }+\left (-1+t \right ) y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.253
4726	25818	\begin{align*} y^{\prime }-\left (y-1\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
4727	3202	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.254
4728	3345	\begin{align*} y^{\prime \prime }+2 y^{\prime } y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.254
4729	3854	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.254
4730	8028	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.254
4731	9222	\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
4732	9351	\begin{align*} y^{\prime }-y&=2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.254
4733	9727	\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
4734	10667	\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
4735	10699	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
4736	10805	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
4737	10882	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
4738	11023	\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*}	✓	✓	✓	✗	0.254
4739	12544	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
4740	12804	\begin{align*} 6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
4741	13148	\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.254
4742	16504	\begin{align*} 16 y^{\prime \prime }-24 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
4743	18318	\begin{align*} \left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y&=\frac {\left (x -1\right )^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	0.254
4744	19050	\begin{align*} x_{1}^{\prime }&=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.254
4745	20900	\begin{align*} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.254
4746	22183	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.254
4747	24587	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.254
4748	25106	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
4749	1307	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
4750	2566	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
4751	7460	\begin{align*} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
4752	8329	\begin{align*} y^{\prime }&=\left (y-2\right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.255
4753	10957	\begin{align*} \left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
4754	14116	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.255
4755	14632	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.255
4756	18379	\begin{align*} y^{\prime }-2 y x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.255
4757	19599	\begin{align*} x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.255
4758	20391	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x +y^{\prime } y+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
4759	22623	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.255
4760	22913	\begin{align*} x^{\prime }-x+2 y^{\prime }+7 y&=0 \\ 2 x^{\prime }+y^{\prime }+x+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
4761	24079	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.255
4762	24600	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.255
4763	24747	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.255
4764	291	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.256
4765	1381	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
4766	3569	\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
4767	3925	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.256
4768	4002	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
4769	6331	\begin{align*} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.256
4770	6513	\begin{align*} 2 x y y^{\prime \prime }&=-y^{\prime } y+x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.256
4771	7050	\begin{align*} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
4772	9461	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.256
4773	10661	\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4774	10773	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4775	10884	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4776	10885	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4777	10963	\begin{align*} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4778	11004	\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4779	12567	\begin{align*} x^{3} y^{\prime \prime }+y^{\prime } x -\left (2 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
4780	13014	\begin{align*} 2 y^{3} y^{\prime \prime }+y^{4}-y^{2} a^{2} x -1&=0 \\ \end{align*}	✗	✗	✗	✗	0.256
4781	14797	\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.256
4782	16024	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.256
4783	16722	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
4784	16820	\begin{align*} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
4785	23711	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
4786	24598	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.256
4787	24642	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.256
4788	441	\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 \(x=0\).	✓	✓	✓	✓	0.257
4789	1304	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
4790	1759	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.257
4791	1766	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✗	0.257
4792	1769	\begin{align*} 2 y^{\prime \prime } x +\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y&=3 \sqrt {x}\, {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.257
4793	2294	\begin{align*} y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.257
4794	2366	\begin{align*} 3 y^{\prime \prime }+6 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
4795	2386	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
4796	2413	\begin{align*} y^{\prime \prime }-t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.257
4797	3065	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
4798	6584	\begin{align*} y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
4799	7061	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
4800	7633	\begin{align*} z^{\prime }-x^{2} z&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.257