2.3.48 Problems 4701 to 4800

Table 2.669: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4701	2419	\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*} Series expansion around \(t=-1\).	✓	✓	✓	✓	0.329
4702	3175	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.329
4703	3570	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4704	3880	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.329
4705	6028	\begin{align*} \left (a \left (1+a \right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4706	9317	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4707	10358	\begin{align*} y^{\prime } x +y&=\tan \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.329
4708	10626	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4709	10705	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4710	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*}	✓	✓	✓	✗	0.329
4711	14292	\begin{align*} \frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.329
4712	14397	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.329
4713	16195	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.329
4714	18195	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.329
4715	18693	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.329
4716	18916	\begin{align*} y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.329
4717	20330	\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4718	20486	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4719	21126	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.329
4720	22194	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4721	23587	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.329
4722	24008	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4723	24593	\begin{align*} y^{\prime \prime }-y&=16 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.329
4724	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*}	✓	✓	✓	✓	0.329
4725	25911	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4726	26444	\begin{align*} y^{\prime \prime \prime }&=\frac {x}{\left (2+x \right )^{5}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.329
4727	27646	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.329
4728	27755	\begin{align*} y^{\prime }&=y+x \,{\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4729	3420	\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.330
4730	5791	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4731	6020	\begin{align*} \left (\operatorname {b2} \,x^{2}+\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4732	8817	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4733	10563	\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4734	10794	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4735	14387	\begin{align*} x^{\prime }&=-6 y \\ y^{\prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	0.330
4736	17583	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.330
4737	17673	\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4738	18103	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.330
4739	18689	\begin{align*} x^{\prime }&=2 x+\frac {y}{2} \\ y^{\prime }&=-\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.330
4740	18782	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.330
4741	19580	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.330
4742	19825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4743	21134	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.330
4744	23632	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.330
4745	24009	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.330
4746	24040	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (3 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4747	1092	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.331
4748	1466	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4749	2597	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.331
4750	2605	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.331
4751	8576	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.331
4752	8940	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.331
4753	9173	\begin{align*} y+\left (x -2 x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4754	10531	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4755	14070	\begin{align*} y y^{\prime }&=\left (-b +x \right ) {y^{\prime }}^{2}+a \\ \end{align*}	✓	✓	✓	✗	0.331
4756	15208	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= -20 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4757	17579	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.331
4758	18280	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.331
4759	21517	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.331
4760	22298	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.331
4761	24675	\begin{align*} 4 y^{\prime \prime }+y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.331
4762	25041	\begin{align*} y^{\prime }&=t^{2}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.331
4763	433	\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
4764	811	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
4765	1074	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4766	2227	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=4 x \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 4 \\ y^{\prime \prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.332
4767	2569	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.332
4768	2734	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.332
4769	3404	\begin{align*} y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\ \end{align*}	✓	✓	✓	✓	0.332
4770	4152	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.332
4771	4590	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4772	6367	\begin{align*} y^{\prime \prime }&=f \left (x , \frac {y^{\prime }}{y}\right ) y \\ \end{align*}	✗	✗	✗	✗	0.332
4773	6718	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.332
4774	7451	\begin{align*} y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4775	9634	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4776	10774	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4777	10910	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4778	10990	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4779	12790	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4780	14101	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.332
4781	15475	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.332
4782	15476	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.332
4783	15516	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.332
4784	16036	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4785	16956	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.332
4786	18687	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}	✓	✓	✓	✓	0.332
4787	18691	\begin{align*} x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.332
4788	21527	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.332
4789	21539	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.332
4790	21942	\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 \(x=0\).	✓	✓	✓	✓	0.332
4791	23523	\begin{align*} e i u^{\prime \prime \prime \prime }&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.332
4792	24647	\begin{align*} 4 y^{\prime \prime }+y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.332
4793	24658	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=21 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.332
4794	24812	\begin{align*} y^{\prime } \left (y^{\prime } x -y+k \right )+a&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4795	26935	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4796	1096	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4797	2420	\begin{align*} y^{\prime \prime }-2 y^{\prime } t +\lambda y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.333
4798	3113	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.333
4799	3232	\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\ \end{align*}	✓	✓	✓	✓	0.333
4800	9065	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.333