2.3.39 Problems 3801 to 3900

Table 2.621: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3801	15513	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.257
3802	16500	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
3803	16709	\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
3804	18280	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.257
3805	18381	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.257
3806	19866	\begin{align*} 4 y^{\prime }+5 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=-\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.257
3807	21219	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.257
3808	22229	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (\pi \right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.257
3809	420	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.258
3810	588	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.258
3811	3951	\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.258
3812	6936	\begin{align*} y^{2}+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.258
3813	8019	\begin{align*} y^{\prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.258
3814	8554	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.258
3815	14614	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.258
3816	17743	\begin{align*} 20 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.258
3817	18385	\begin{align*} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.258
3818	20936	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.258
3819	437	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.259
3820	1396	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.259
3821	1767	\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=\left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.259
3822	3948	\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.	✓	✓	✓	✓	0.259
3823	5921	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=x^{2}-x -1 \\ \end{align*}	✓	✓	✓	✗	0.259
3824	9314	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.259
3825	18231	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x -2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.259
3826	20395	\begin{align*} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.259
3827	21139	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=2 t +{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.259
3828	21210	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.259
3829	23008	\begin{align*} 35 y^{\prime \prime }-29 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.259
3830	24021	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.259
3831	25642	\begin{align*} y^{\prime \prime }+B y^{\prime }+C y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.259
3832	421	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.260
3833	587	\begin{align*} x^{\prime }&=-x+3 y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.260
3834	1771	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=4 x^{{5}/{2}} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.260
3835	2314	\begin{align*} y^{\prime }+\frac {y}{\sqrt {t}}&={\mathrm e}^{\frac {\sqrt {t}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.260
3836	2316	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.260
3837	3099	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3838	3617	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.260
3839	7969	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.260
3840	7972	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.260
3841	8794	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3842	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*}	✓	✓	✓	✗	0.260
3843	10662	\begin{align*} 2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3844	10891	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3845	10978	\begin{align*} x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3846	12817	\begin{align*} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+{\mathrm e}^{x} y-\frac {1}{x^{5}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3847	14341	\begin{align*} x^{\prime \prime }-2 a x^{\prime }+a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3848	15002	\begin{align*} x^{\prime }&=11 x-2 y \\ y^{\prime }&=3 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.260
3849	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.	✓	✓	✓	✓	0.260
3850	16505	\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3851	17412	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3852	18343	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3853	18898	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.260
3854	23003	\begin{align*} 3 x^{\prime \prime }+19 x^{\prime }-14 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3855	24087	\begin{align*} \left (x^{3}-8\right ) y^{\prime \prime }-4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.260
3856	25938	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.260
3857	25958	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.260
3858	25963	\begin{align*} y^{\prime \prime }+y&=x^{5}-2 x^{2}+6 \\ \end{align*}	✓	✓	✓	✓	0.260
3859	5799	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3860	5803	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3861	9452	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
3862	10590	\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
3863	13166	\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.261
3864	13169	\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.261
3865	16504	\begin{align*} 16 y^{\prime \prime }-24 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3866	22096	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3867	23010	\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3868	23404	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3869	25070	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
3870	405	\begin{align*} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
3871	3407	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.262
3872	6149	\begin{align*} 12 y+2 \left (3-4 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3873	8174	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.262
3874	8606	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
3875	9113	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.262
3876	10461	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3877	10716	\begin{align*} y^{\prime \prime } x +\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3878	14111	\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.262
3879	16722	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3880	16728	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3881	18195	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.262
3882	18283	\begin{align*} y^{\prime \prime }-y&=-2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.262
3883	18780	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3884	21485	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3885	23007	\begin{align*} 20 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3886	23421	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3887	23430	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3888	24778	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3889	342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.263
3890	385	\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.263
3891	408	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
3892	1738	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= k_{0} \\ y^{\prime }\left (0\right ) &= k_{1} \\ \end{align*}	✓	✓	✓	✓	0.263
3893	2296	\begin{align*} 2 t y+y^{\prime }&=t \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.263
3894	3624	\begin{align*} y^{\prime }+\frac {2 y}{x}&=4 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.263
3895	3947	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.263
3896	4120	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3897	8099	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.263
3898	10736	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3899	11727	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3900	15086	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.263