2.3.39 Problems 3801 to 3900

Table 2.609: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3801	8122	\begin{align*} y^{\prime \prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.214
3802	8966	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.214
3803	9353	\begin{align*} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.214
3804	9355	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.214
3805	9620	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=t +1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.214
3806	10515	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
3807	11054	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
3808	11119	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
3809	13673	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
3810	14206	\begin{align*} x^{\prime }&=t \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.214
3811	16052	\(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.214
3812	16184	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ \end{align*}	✓	✓	✓	✓	0.214
3813	16211	\begin{align*} y^{\prime }&=\sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	0.214
3814	16823	\begin{align*} \left (x -3\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.214
3815	17382	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.214
3816	23017	\begin{align*} y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.214
3817	3989	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.215
3818	6455	\begin{align*} g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.215
3819	9036	\begin{align*} y y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
3820	9462	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.215
3821	10659	\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
3822	10727	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
3823	10825	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
3824	11002	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
3825	11060	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
3826	11737	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3827	12850	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.215
3828	15683	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.215
3829	16459	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.215
3830	16847	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.215
3831	17390	\begin{align*} 4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3832	18741	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3833	22103	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3834	22795	\begin{align*} x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=\frac {\ln \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	0.215
3835	23029	\begin{align*} x^{\prime \prime }-2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3836	23345	\begin{align*} y^{\prime \prime }-i y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3837	23717	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.215
3838	24118	\begin{align*} y^{\prime }-y&=x^{2}+1 \\ y \left (0\right ) &= -3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.215
3839	25085	\begin{align*} y^{\prime \prime }+4 y&=32 \cos \left (2 t \right ) t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.215
3840	25805	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
3841	5966	\begin{align*} -\left (a \left (a -1\right )-b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.216
3842	7821	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.216
3843	8130	\begin{align*} y^{\prime \prime }+2 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.216
3844	10829	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.216
3845	10979	\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.216
3846	11097	\begin{align*} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align*}	✓	✓	✓	✓	0.216
3847	15698	\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.216
3848	16985	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.216
3849	17391	\begin{align*} 7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.216
3850	17417	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.216
3851	22194	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.216
3852	23110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.216
3853	24585	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.216
3854	405	\begin{align*} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.217
3855	1397	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.217
3856	1758	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.217
3857	2173	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \\ \end{align*}	✓	✓	✓	✓	0.217
3858	3061	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3859	3207	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.217
3860	5380	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3861	5518	\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+4 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3862	6511	\begin{align*} a y^{\prime } \left (-y+y^{\prime } x \right )+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3863	7260	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3864	7589	\begin{align*} z^{\prime \prime }+z^{\prime }-z&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3865	7720	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.217
3866	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.	✓	✓	✓	✓	0.217
3867	9616	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.217
3868	10332	\begin{align*} t y^{\prime }+y&=t \\ y \left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	0.217
3869	10511	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3870	10629	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3871	10635	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3872	10767	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3873	10827	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3874	10831	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3875	11052	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3876	11098	\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3877	12546	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
3878	13008	\begin{align*} x y^{2} y^{\prime \prime }-a&=0 \\ \end{align*}	✗	✓	✓	✗	0.217
3879	14772	\begin{align*} x^{\prime }+y^{\prime }-x&=-2 t \\ x^{\prime }+y^{\prime }-3 x-y&=t^{2} \\ \end{align*}	✓	✓	✓	✗	0.217
3880	15686	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=6 x -20-120 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.217
3881	16163	\begin{align*} y^{\prime }&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.217
3882	16314	\begin{align*} {\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3883	16464	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.217
3884	17359	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3885	17741	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3886	17743	\begin{align*} 20 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3887	18774	\begin{align*} y^{\prime \prime }-9 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3888	19842	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=x \\ \end{align*}	✓	✓	✓	✓	0.217
3889	22109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3890	22644	\begin{align*} 4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3891	24512	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
3892	407	\begin{align*} 2 \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.218
3893	1080	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.218
3894	2175	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.218
3895	5561	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3896	6152	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3897	7452	\begin{align*} 2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
3898	8019	\begin{align*} y^{\prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.218
3899	8964	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.218
3900	9453	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.218