2.3.37 Problems 3601 to 3700

Table 2.647: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3601	23609	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.294
3602	24413	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
3603	27159	\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.294
3604	27561	\begin{align*} y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.294
3605	239	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
3606	1269	\begin{align*} y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
3607	1276	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
3608	13143	\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.295
3609	13144	\(\left [\begin {array}{cc} 10 & -8 \\ 6 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.295
3610	15707	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x +\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.295
3611	26013	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.295
3612	521	\begin{align*} 4 x^{2} y^{\prime \prime }-12 x y^{\prime }+\left (15+16 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3613	858	\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3614	1068	\begin{align*} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.296
3615	1312	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3616	2545	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3617	3064	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3618	3308	\begin{align*} x&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.296
3619	3922	\begin{align*} x_{1}^{\prime }&=-4 x_{1} \\ x_{2}^{\prime }&=-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.296
3620	7221	\begin{align*} x y y^{\prime }-y x&=y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.296
3621	7237	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y x +2 x \sqrt {-x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	0.296
3622	7967	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3623	10993	\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.296
3624	13172	\(\left [\begin {array}{cc} 5 & -4 \\ 2 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.296
3625	13173	\(\left [\begin {array}{cc} 6 & -6 \\ 4 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.296
3626	16463	\begin{align*} x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.296
3627	16464	\begin{align*} \left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.296
3628	16774	\begin{align*} y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.296
3629	22736	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.296
3630	23145	\begin{align*} y y^{\prime }&=x^{3} y^{2}+x y^{2} \\ \end{align*}	✓	✓	✓	✓	0.296
3631	23444	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.296
3632	26481	\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
3633	27158	\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=5 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.296
3634	235	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
3635	242	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
3636	243	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
3637	1768	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=4 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.297
3638	6582	\begin{align*} {y^{\prime \prime }}^{2}&=a +b y \\ \end{align*}	✗	✓	✓	✗	0.297
3639	10741	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
3640	10981	\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.297
3641	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*}	✓	✓	✓	✗	0.297
3642	11076	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.297
3643	13147	\(\left [\begin {array}{cc} 9 & -10 \\ 2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.297
3644	19627	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-x} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.297
3645	23030	\begin{align*} z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
3646	23665	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=13 t +17+40 \sin \left (t \right ) \\ y \left (0\right ) &= 30 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.297
3647	26718	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9}&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
3648	853	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.298
3649	1256	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.298
3650	1377	\begin{align*} y^{\prime \prime }-x y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.298
3651	3589	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.298
3652	10546	\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.298
3653	10737	\begin{align*} -a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.298
3654	10992	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.298
3655	11852	\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✗	0.298
3656	12771	\begin{align*} 4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	0.298
3657	19630	\begin{align*} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✗	0.298
3658	23801	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.298
3659	26706	\begin{align*} 4 x y^{\prime }+2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.298
3660	391	\begin{align*} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.299
3661	1060	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.299
3662	2672	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.299
3663	7623	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.299
3664	10471	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.299
3665	10651	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.299
3666	12760	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (8+x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
3667	13176	\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.299
3668	15700	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.299
3669	21910	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.299
3670	23110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
3671	23639	\begin{align*} y^{\prime \prime \prime }-27 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ y^{\prime \prime }\left (0\right ) &= 18 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.299
3672	23760	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.299
3673	23803	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.299
3674	26355	\begin{align*} x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\ \end{align*}	✓	✓	✓	✓	0.299
3675	1363	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.300
3676	6679	\begin{align*} 2 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.300
3677	7831	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ 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.	✓	✓	✓	✓	0.300
3678	9129	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.300
3679	9446	\begin{align*} L i^{\prime }+R i&=E_{0} \delta \left (t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.300
3680	11018	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.300
3681	18260	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✓	0.300
3682	20553	\begin{align*} x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.300
3683	22652	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.300
3684	23334	\begin{align*} 8 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.300
3685	23661	\begin{align*} y^{\prime \prime \prime }+y&=18 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.300
3686	24050	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.300
3687	849	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
3688	1379	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.301
3689	4493	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.301
3690	7453	\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
3691	10597	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.301
3692	10756	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
3693	12599	\begin{align*} y^{\prime \prime }&=-\frac {\left (-3 x +1\right ) y}{\left (x -1\right ) \left (2 x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.301
3694	12600	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (x +a \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (x +a \right )^{2} \left (x +b \right )} \\ \end{align*}	✓	✓	✓	✗	0.301
3695	13141	\(\left [\begin {array}{cc} 4 & -3 \\ 2 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.301
3696	23443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.301
3697	27088	\(\left [\begin {array}{cc} 1 & 3 \\ 2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.301
3698	329	\begin{align*} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.302
3699	2296	\begin{align*} 2 y t +y^{\prime }&=t \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.302
3700	3228	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	0.302