2.3.40 Problems 3901 to 4000

Table 2.611: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3901	10342	\begin{align*} t^{2} y+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.218
3902	10610	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
3903	10619	\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
3904	10700	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
3905	12892	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\ \end{align*}	✗	✗	✗	✗	0.218
3906	13779	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3907	15147	\begin{align*} y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3908	16558	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3909	16824	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.218
3910	16853	\begin{align*} y^{\prime }+\cos \left (y\right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.218
3911	17744	\begin{align*} 12 y^{\prime \prime }+8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3912	18958	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.218
3913	19169	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3914	20588	\begin{align*} x^{2} y^{\prime \prime }+4 y^{2}-6 y&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.218
3915	20837	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3916	22676	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3917	23314	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
3918	24673	\begin{align*} y^{\prime \prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.218
3919	1079	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.219
3920	2212	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.219
3921	3762	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {2 \,{\mathrm e}^{x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.219
3922	5899	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
3923	8628	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= {\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.219
3924	10833	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
3925	10983	\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
3926	11071	\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*}	✓	✓	✓	✗	0.219
3927	13668	\begin{align*} y^{\prime \prime }-a \,x^{n} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
3928	14635	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \\ \end{align*}	✓	✓	✓	✓	0.219
3929	16493	\begin{align*} 3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
3930	17385	\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
3931	19576	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.219
3932	20008	\begin{align*} x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
3933	20147	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.219
3934	21888	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=x^{3}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.219
3935	21999	\begin{align*} \frac {1}{x}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
3936	23028	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
3937	23705	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.219
3938	1097	\begin{align*} y^{\prime \prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.220
3939	1524	\begin{align*} y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.220
3940	1772	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.220
3941	2174	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.220
3942	5577	\begin{align*} y^{2} {y^{\prime }}^{2}+2 x y^{\prime } y+a -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3943	6479	\begin{align*} 2 y y^{\prime \prime }&=-1+2 x f \left (x \right ) y^{2}-y^{4}-4 y^{2} y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.220
3944	6684	\begin{align*} 6 n y^{\prime }-2 \left (n +1\right ) x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3945	6853	\begin{align*} n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3946	8067	\begin{align*} \left (1-x \right ) y^{\prime }&=x^{2}-y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.220
3947	9632	\begin{align*} -y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.220
3948	10423	\begin{align*} 10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y}&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3949	10480	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3950	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*}	✓	✓	✓	✗	0.220
3951	11080	\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3952	11109	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
3953	11293	\begin{align*} y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	0.220
3954	12552	\begin{align*} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
3955	15250	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.220
3956	17742	\begin{align*} 15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
3957	19763	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.220
3958	19834	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.220
3959	22031	\begin{align*} 3 y^{2} x^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
3960	23031	\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
3961	523	\begin{align*} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x -2 \left (-x^{5}+14\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3962	552	\begin{align*} x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.221
3963	2185	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y&={\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.221
3964	4589	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.221
3965	5550	\begin{align*} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3966	5789	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3967	5797	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3968	8037	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
3969	8358	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	0.221
3970	9173	\begin{align*} y+\left (x -2 x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
3971	10624	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
3972	10932	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
3973	11685	\begin{align*} {y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3974	12653	\begin{align*} y^{\prime \prime }&=-\frac {3 y}{16 x^{2} \left (x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.221
3975	16768	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.221
3976	17739	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3977	19547	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3978	20392	\begin{align*} {y^{\prime }}^{3}-y^{\prime } \left (x^{2}+y x +y^{2}\right )+x y \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3979	20705	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.221
3980	21890	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.221
3981	23327	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3982	25079	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.221
3983	25512	\begin{align*} 2 t y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
3984	1768	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.222
3985	5890	\begin{align*} -y+y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
3986	10928	\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*}	✓	✓	✓	✗	0.222
3987	11057	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
3988	11236	\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
3989	11292	\begin{align*} y^{\prime \prime }&=\left (\frac {6}{x^{2}}-1\right ) y \\ \end{align*}	✓	✓	✓	✓	0.222
3990	12732	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
3991	17736	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
3992	22249	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.222
3993	22337	\begin{align*} 1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
3994	22642	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
3995	22822	\begin{align*} y^{\prime }&=y x \\ y \left (0\right ) &= 5 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.222
3996	408	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.223
3997	546	\begin{align*} x^{\prime \prime \prime \prime }-x&=0 \\ x \left (0\right ) &= 1 \\ 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.	✓	✓	✓	✓	0.223
3998	852	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
3999	5387	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4000	5395	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.223