2.3.37 Problems 3601 to 3700

Table 2.605: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3601	6498	\begin{align*} x y y^{\prime \prime }&=y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y^{\prime } y+x {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.204
3602	7140	\begin{align*} y^{\prime } y-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
3603	7262	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3604	7912	\begin{align*} 3 y^{2} x^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
3605	8124	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.204
3606	8173	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3607	9239	\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3608	9450	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
3609	10242	\begin{align*} y^{\prime }+y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.204
3610	10344	\begin{align*} y^{\prime }+\left (a t +b t \right ) y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
3611	10554	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3612	10744	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
3613	11111	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
3614	11214	\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3615	14577	\begin{align*} 3 y^{\prime \prime }-14 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3616	14779	\begin{align*} x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
3617	15703	\begin{align*} y^{\prime \prime }-9 y&=2+x \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
3618	17647	\begin{align*} x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.204
3619	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*}	✓	✓	✓	✓	0.204
3620	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*}	✓	✓	✓	✓	0.204
3621	21590	\begin{align*} y^{\left (5\right )}+y^{\prime \prime }&=x^{5}-3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.204
3622	24590	\begin{align*} y^{\prime \prime }-y&=2 x -3 \\ \end{align*}	✓	✓	✓	✓	0.204
3623	25534	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+\omega ^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
3624	1396	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.205
3625	4666	\begin{align*} y^{\prime }&=3 a +3 b x +3 b y^{2} \\ \end{align*}	✓	✓	✓	✗	0.205
3626	6953	\begin{align*} {\mathrm e}^{x} \left (x +1\right )+\left (-x \,{\mathrm e}^{x}+{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.205
3627	8071	\begin{align*} \left (x +1\right ) y^{\prime }&=x^{2}-2 x +y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.205
3628	9363	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.205
3629	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.	✓	✓	✓	✓	0.205
3630	9714	\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.205
3631	10775	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.205
3632	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*}	✓	✓	✓	✗	0.205
3633	16167	\begin{align*} y^{\prime }&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.205
3634	19564	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.205
3635	21882	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=2 x^{2}-3 x -17 \\ \end{align*}	✓	✓	✓	✓	0.205
3636	23834	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{t \left (t -2\right )} \\ \end{align*}	✓	✓	✓	✓	0.205
3637	25254	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.205
3638	3060	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.206
3639	8892	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.206
3640	10471	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.206
3641	15496	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.206
3642	15706	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.206
3643	15711	\begin{align*} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.206
3644	23675	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.206
3645	23825	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.206
3646	23832	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {t^{2}+2 t}} \\ \end{align*}	✓	✓	✓	✓	0.206
3647	25081	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \cos \left (t \right )+\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.206
3648	279	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3649	530	\begin{align*} x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
3650	657	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.207
3651	857	\begin{align*} y^{\prime \prime }-2 i y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3652	1042	\begin{align*} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.207
3653	1046	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.207
3654	1280	\begin{align*} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3655	1634	\begin{align*} y^{\prime }-\frac {\left (x +1\right ) y}{3 x}&=y^{4} \\ \end{align*}	✓	✓	✓	✓	0.207
3656	2774	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.207
3657	3985	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.207
3658	5522	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.207
3659	9741	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3660	10352	\begin{align*} y^{\prime } x +y&=2 x^{4}+x^{3}+x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.207
3661	10592	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
3662	10747	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
3663	11120	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3664	11130	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
3665	12712	\begin{align*} y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3666	15413	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.207
3667	16152	\begin{align*} y^{\prime }&=3-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.207
3668	16166	\begin{align*} y^{\prime }&=x \cos \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.207
3669	16181	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.207
3670	16721	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3671	16819	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
3672	17380	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3673	18891	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\cos \left (2 t \right ) t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
3674	22643	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3675	23258	\begin{align*} y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.207
3676	25255	\begin{align*} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
3677	4122	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
3678	4492	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }-4 y&=50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.208
3679	5814	\begin{align*} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
3680	6885	\begin{align*} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.208
3681	9063	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.208
3682	10596	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
3683	11021	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
3684	14150	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
3685	15144	\begin{align*} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=y x \\ \end{align*}	✗	✗	✗	✗	0.208
3686	23662	\begin{align*} y^{\prime \prime \prime }+8 y&=-12 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= -8 \\ y^{\prime }\left (0\right ) &= 24 \\ y^{\prime \prime }\left (0\right ) &= -46 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.208
3687	23716	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.208
3688	23975	\begin{align*} y^{\prime \prime }-2 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
3689	24601	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.208
3690	24850	\begin{align*} y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
3691	25080	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.208
3692	278	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
3693	3059	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
3694	3062	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
3695	5815	\begin{align*} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
3696	7632	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.209
3697	9215	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
3698	10052	\begin{align*} 3 y y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.209
3699	10259	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
3700	10763	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.209