2.3.39 Problems 3801 to 3900

Table 2.651: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3801	17597	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{t}}{t} \\ \end{align*}	✓	✓	✓	✓	0.310
3802	18329	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=\frac {x -1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.310
3803	22651	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.310
3804	23315	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
3805	23438	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.310
3806	25996	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.310
3807	27778	\begin{align*} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.310
3808	2364	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.311
3809	7064	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.311
3810	8143	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.311
3811	10544	\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.311
3812	11853	\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.311
3813	15985	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.311
3814	17596	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=-\frac {1}{t^{2}}-\frac {2}{t} \\ \end{align*}	✓	✓	✓	✓	0.311
3815	26010	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.311
3816	27123	\(\left [\begin {array}{cc} -13 & 1 \\ 1 & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.311
3817	1279	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
3818	1374	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.312
3819	10059	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.312
3820	10603	\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*}	✓	✓	✓	✗	0.312
3821	10604	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.312
3822	10778	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
3823	16786	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.312
3824	18462	\begin{align*} x^{\prime \prime }&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.312
3825	19049	\begin{align*} x_{1}^{\prime }&=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.312
3826	23802	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.312
3827	24410	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
3828	26244	\begin{align*} \ln \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.312
3829	1452	\begin{align*} x_{1}^{\prime }&=-x_{1} \\ x_{2}^{\prime }&=-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.313
3830	1756	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.313
3831	2546	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
3832	4463	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }&=7 x -3 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.313
3833	7834	\begin{align*} q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2} \\ q \left (0\right ) &= 0 \\ q^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.313
3834	7900	\begin{align*} y-\ln \left (x \right )-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
3835	8072	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.313
3836	10344	\begin{align*} y^{\prime }+\left (a t +b t \right ) y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.313
3837	10507	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
3838	10570	\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*}	✓	✓	✓	✗	0.313
3839	10598	\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*}	✓	✓	✓	✗	0.313
3840	10714	\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
3841	10750	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
3842	10766	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
3843	10948	\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
3844	16779	\begin{align*} y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.313
3845	18985	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
3846	20383	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
3847	22746	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \\ \end{align*}	✓	✓	✓	✓	0.313
3848	23656	\begin{align*} y^{\prime \prime \prime }-y&=12 \sinh \left (t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.313
3849	23716	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.313
3850	26050	\begin{align*} {y^{\prime }}^{3}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
3851	27751	\begin{align*} y^{\prime \prime }-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
3852	3066	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
3853	9115	\begin{align*} y x +x^{2} y^{\prime }&=2 x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.314
3854	10644	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.314
3855	11165	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
3856	23612	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.314
3857	27107	\(\left [\begin {array}{cc} -13 & 1 \\ 1 & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.314
3858	27731	\begin{align*} x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
3859	412	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.315
3860	3273	\begin{align*} y^{\prime \prime }&=y^{3} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✗	0.315
3861	3340	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (2\right ) &= 0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.315
3862	3953	\begin{align*} y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.315
3863	9614	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.315
3864	10049	\begin{align*} y y^{\prime \prime }&=x \\ \end{align*}	✗	✗	✗	✗	0.315
3865	10543	\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*}	✓	✓	✓	✗	0.315
3866	10867	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.315
3867	12676	\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x \left (\ln \left (x \right )-1\right )}-\frac {y}{x^{2} \left (\ln \left (x \right )-1\right )} \\ \end{align*}	✓	✓	✓	✗	0.315
3868	13177	\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.315
3869	14626	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y&=-18 x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.315
3870	16765	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.315
3871	19021	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.315
3872	20697	\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
3873	26101	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
3874	26626	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	0.315
3875	27667	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.315
3876	27668	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-x} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.315
3877	518	\begin{align*} 36 x^{2} y^{\prime \prime }+60 x y^{\prime }+\left (9 x^{3}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
3878	550	\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&={\mathrm e}^{2 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.316
3879	1078	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
3880	7837	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
3881	7897	\begin{align*} 2 y-3 x +x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
3882	10423	\begin{align*} 10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y}&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
3883	10655	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
3884	11024	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
3885	13179	\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.316
3886	17732	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
3887	17739	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
3888	21205	\begin{align*} x^{\prime }&=a x \\ y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	0.316
3889	22720	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.316
3890	23031	\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
3891	26011	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
3892	26055	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
3893	27066	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
3894	27143	\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=5 x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.316
3895	1009	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.317
3896	1760	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=7 x^{{3}/{2}} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.317
3897	7728	\begin{align*} y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.317
3898	7804	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=\frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.317
3899	8792	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.317
3900	9226	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.317