2.3.38 Problems 3701 to 3800

Table 2.619: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3701	20490	\begin{align*} x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x -4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
3702	20893	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.251
3703	22791	\begin{align*} s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.251
3704	23264	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.251
3705	24029	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=x^{2}+4 x +3 \\ \end{align*}	✓	✓	✓	✓	0.251
3706	381	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✗	0.252
3707	3284	\begin{align*} 4 y^{2}&=x^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.252
3708	3944	\begin{align*} y^{\prime \prime }-y&=6 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.252
3709	3949	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.252
3710	7584	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
3711	10329	\begin{align*} x^{\prime }+y^{\prime }-x&=y+t \\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✗	0.252
3712	10778	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
3713	10937	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
3714	13168	\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.252
3715	15064	\begin{align*} {y^{\prime }}^{2}+\left (a +x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
3716	16462	\begin{align*} x^{2} y^{\prime \prime }-20 y&=27 x^{5} \\ \end{align*}	✓	✓	✓	✓	0.252
3717	18317	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	0.252
3718	23002	\begin{align*} y^{\prime \prime }+7 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
3719	428	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
3720	1044	\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
3721	1760	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=7 x^{{3}/{2}} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.253
3722	1766	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✗	0.253
3723	3946	\begin{align*} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.253
3724	8031	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
3725	9110	\begin{align*} y^{\prime }-y x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.253
3726	9487	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
3727	10559	\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*}	✓	✓	✓	✗	0.253
3728	12594	\begin{align*} y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \\ \end{align*}	✓	✓	✓	✗	0.253
3729	14345	\begin{align*} x^{\prime \prime \prime }+x^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.253
3730	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*}	✓	✓	✓	✓	0.253
3731	17586	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \\ \end{align*}	✓	✓	✓	✓	0.253
3732	17604	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=3 t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.253
3733	18456	\begin{align*} x^{\prime }+3 x&={\mathrm e}^{-2 t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.253
3734	18984	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
3735	21146	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.253
3736	22105	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
3737	23000	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
3738	23005	\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
3739	25910	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
3740	395	\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.254
3741	423	\begin{align*} y^{\prime \prime }&=y^{\prime }+y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.254
3742	577	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.254
3743	7802	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.254
3744	10741	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3745	12413	\begin{align*} x^{2} y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3746	16716	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3747	17627	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3748	17732	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3749	20095	\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3750	20386	\begin{align*} y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.254
3751	20789	\begin{align*} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
3752	20901	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.254
3753	21280	\begin{align*} x^{\prime }+x&={\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.254
3754	22625	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \\ \end{align*}	✓	✓	✓	✓	0.254
3755	23459	\begin{align*} y^{\prime \prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.254
3756	25321	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.254
3757	392	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.255
3758	7588	\begin{align*} 6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3759	7881	\begin{align*} x^{2}-y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3760	9613	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.255
3761	9882	\begin{align*} 9 x^{2} y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3762	11020	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
3763	15003	\begin{align*} x^{\prime }&=x+20 y \\ y^{\prime }&=40 x-19 y \\ \end{align*}	✓	✓	✓	✓	0.255
3764	17588	\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y&=153 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.255
3765	17742	\begin{align*} 15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3766	18762	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3767	20157	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	0.255
3768	20943	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.255
3769	21220	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.255
3770	24470	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3771	1326	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3772	3417	\begin{align*} y^{\prime }&=t^{2}+3 \\ \end{align*}	✓	✓	✓	✓	0.256
3773	8632	\begin{align*} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {63}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3774	10776	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3775	11685	\begin{align*} {y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3776	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.	✓	✓	✓	✓	0.256
3777	16463	\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.256
3778	16502	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3779	17382	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3780	18759	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3781	19469	\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3782	21095	\begin{align*} {x^{\prime }}^{2}&=-4 x+4 \\ \end{align*}	✓	✓	✓	✓	0.256
3783	21705	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{5 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3784	22103	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3785	22231	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3786	24018	\begin{align*} y^{\prime \prime \prime }+3 k y^{\prime \prime }+3 k^{2} y^{\prime }+k^{3} y&={\mathrm e}^{-k x} f^{\prime \prime \prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.256
3787	24022	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.256
3788	25066	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3789	25078	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3790	403	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.257
3791	435	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.257
3792	441	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.257
3793	1061	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.257
3794	2218	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-x} \left (20-12 x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ y^{\prime \prime }\left (0\right ) &= 7 \\ y^{\prime \prime \prime }\left (0\right ) &= -22 \\ \end{align*}	✓	✓	✓	✓	0.257
3795	3789	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=8 x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.257
3796	6768	\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
3797	8281	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.257
3798	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*}	✓	✓	✓	✗	0.257
3799	11853	\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3800	12706	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.257