2.3.41 Problems 4001 to 4100

Table 2.655: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4001	12706	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.325
4002	13184	\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.325
4003	14565	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4004	14773	\begin{align*} x^{\prime }+y^{\prime }-x-3 y&={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✗	0.325
4005	22336	\begin{align*} {| y^{\prime }|}+1&=0 \\ \end{align*}	✗	✓	✗	✗	0.325
4006	25104	\begin{align*} y^{\prime \prime }+13 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4007	27769	\begin{align*} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.325
4008	355	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.326
4009	418	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4010	1091	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4011	1397	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4012	1417	\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.326
4013	1880	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4014	3210	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.326
4015	6731	\begin{align*} y^{\prime \prime \prime \prime }&=x^{3}+a^{4} y \\ \end{align*}	✓	✓	✓	✓	0.326
4016	10515	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4017	11003	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4018	11047	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4019	16722	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4020	16761	\begin{align*} y^{\prime \prime }-4 y&=t^{3} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4021	20018	\begin{align*} {y^{\prime }}^{2}+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4022	21710	\begin{align*} y^{\prime }+b y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4023	23601	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.326
4024	26019	\begin{align*} y^{\prime \prime }+3 x y^{\prime }+7 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4025	26486	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4026	1013	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+9 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.327
4027	1267	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= \alpha \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.327
4028	2176	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&={\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.327
4029	2234	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.327
4030	4253	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4031	5743	\begin{align*} \left (b x +a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4032	7134	\begin{align*} \left (y+1\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	0.327
4033	8124	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.327
4034	14627	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.327
4035	15517	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4036	17737	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4037	17742	\begin{align*} 15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4038	19486	\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4039	20048	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y&=X \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.327
4040	21281	\begin{align*} x^{\prime }+x&=t \\ x \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.327
4041	23980	\begin{align*} y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50}&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4042	27144	\begin{align*} x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.327
4043	27591	\begin{align*} x \left (y^{\prime \prime }+{y^{\prime }}^{2}\right )&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.327
4044	1372	\begin{align*} y^{\prime \prime }-x y^{\prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.328
4045	7720	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.328
4046	10060	\begin{align*} x^{\prime }&=7 x+y \\ y^{\prime }&=-4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.328
4047	10353	\begin{align*} x y^{\prime }+y&=\frac {1}{x^{3}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.328
4048	10717	\begin{align*} x^{4} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
4049	16780	\begin{align*} y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.328
4050	16787	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.328
4051	1306	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4052	2316	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4053	4607	\begin{align*} y^{\prime }&=a f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4054	7830	\begin{align*} y^{\prime \prime \prime }-y&=5 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4055	7841	\begin{align*} y^{\prime \prime }+2 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4056	8753	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4057	9600	\begin{align*} y+2 y^{\prime }&=0 \\ y \left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4058	10014	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4059	10510	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4060	10584	\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4061	10591	\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4062	10652	\begin{align*} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
4063	10740	\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*}	✓	✓	✓	✓	0.329
4064	12601	\begin{align*} y^{\prime \prime }&=\frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}+\frac {y}{3 x^{2} \left (x -2\right )} \\ \end{align*}	✓	✓	✓	✗	0.329
4065	16766	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4066	19825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4067	22240	\begin{align*} y^{\prime }+2 y&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4068	22625	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \\ \end{align*}	✓	✓	✓	✓	0.329
4069	24502	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\infty \right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.329
4070	25101	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4071	27188	\begin{align*} x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.329
4072	27535	\begin{align*} y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4073	1272	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \beta \\ \end{align*}	✓	✓	✓	✗	0.330
4074	1769	\begin{align*} 2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=3 \sqrt {x}\, {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.330
4075	2194	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&={\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.330
4076	7168	\begin{align*} y^{\prime \prime }+a \,x^{2} y&=x +1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.330
4077	8269	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.330
4078	10565	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4079	23109	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {y-y^{\prime }}{x} \\ \end{align*}	✓	✓	✓	✗	0.330
4080	23361	\begin{align*} y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4081	2213	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.331
4082	6925	\begin{align*} 2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4083	8639	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \\ y \left (0\right ) &= {\frac {19}{12}} \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4084	9217	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4085	10840	\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4086	20913	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4087	23006	\begin{align*} y^{\prime \prime }-2 y^{\prime }-63 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.331
4088	23026	\begin{align*} y^{\prime \prime }-5 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4089	23771	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.331
4090	26955	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4091	27736	\begin{align*} 2 x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4092	400	\begin{align*} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4093	517	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4094	1076	\begin{align*} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4095	1077	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4096	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*}	✓	✓	✓	✗	0.332
4097	2223	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.332
4098	3624	\begin{align*} y^{\prime }+\frac {2 y}{x}&=4 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.332
4099	7582	\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4100	7584	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332