2.3.41 Problems 4001 to 4100

Table 2.613: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4001	5607	\begin{align*} {y^{\prime }}^{3}&=b x +a \\ \end{align*}	✓	✓	✓	✓	0.223
4002	5768	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4003	7591	\begin{align*} y^{\prime \prime }-y^{\prime }-11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4004	8142	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.223
4005	9227	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4006	9609	\begin{align*} y+y^{\prime }&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.223
4007	9977	\begin{align*} y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.223
4008	10985	\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*}	✓	✓	✓	✗	0.223
4009	11075	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.223
4010	11215	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4011	11221	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.223
4012	11235	\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4013	16032	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4014	16412	\begin{align*} y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.223
4015	19110	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
4016	22839	\begin{align*} y^{\prime }+y&=x^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.223
4017	23590	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.223
4018	25625	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.223
4019	1275	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
4020	1787	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	0.224
4021	2186	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (x +5\right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.224
4022	3791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.224
4023	4513	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=60 \cos \left (3 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.224
4024	4587	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.224
4025	4591	\begin{align*} y^{\prime \prime }-2 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.224
4026	6406	\begin{align*} -6+x y \left (12+3 y x -2 y^{2} x^{2}\right )+x^{2} \left (9+2 y x \right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.224
4027	8855	\begin{align*} y^{\prime }&={\mathrm e}^{3 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.224
4028	10270	\begin{align*} c y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
4029	10420	\begin{align*} y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4030	10439	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4031	10641	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4032	10682	\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4033	10752	\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4034	10857	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4035	11053	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4036	12960	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+f \left (x \right ) y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.224
4037	13193	\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.224
4038	14402	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.224
4039	15103	\begin{align*} -y^{\prime } y-x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
4040	19759	\begin{align*} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime }&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.224
4041	19845	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.224
4042	21804	\begin{align*} \left (x -y\right ) y^{\prime }&=y-x \\ \end{align*}	✓	✓	✓	✓	0.224
4043	22099	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
4044	23277	\begin{align*} y^{\prime \prime } x -3 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
4045	24027	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\ \end{align*}	✓	✓	✓	✓	0.224
4046	24593	\begin{align*} y^{\prime \prime }-y&=16 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.224
4047	24675	\begin{align*} 4 y^{\prime \prime }+y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.224
4048	24685	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=6 x^{2}-6 x -11 \\ \end{align*}	✓	✓	✓	✓	0.224
4049	24892	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
4050	409	\begin{align*} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.225
4051	3792	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.225
4052	7055	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
4053	9314	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
4054	10631	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
4055	10988	\begin{align*} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
4056	15475	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.225
4057	15697	\begin{align*} y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.225
4058	16829	\begin{align*} \left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.225
4059	18759	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
4060	24116	\begin{align*} y^{\prime }&=x +2 y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.225
4061	24712	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.225
4062	25239	\begin{align*} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.225
4063	25242	\begin{align*} t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.225
4064	2441	\begin{align*} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=2\).	✗	✗	✓	✗	0.226
4065	2546	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4066	5801	\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4067	7052	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4068	8638	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
4069	11234	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
4070	12957	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4}&=0 \\ \end{align*}	✗	✗	✗	✗	0.226
4071	15524	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.226
4072	17731	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4073	17901	\begin{align*} \tan \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.226
4074	18758	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4075	19164	\begin{align*} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 y^{\prime } x -12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4076	20881	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.226
4077	21281	\begin{align*} x^{\prime }+x&=t \\ x \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
4078	22107	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4079	23030	\begin{align*} z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4080	23357	\begin{align*} y^{\prime \prime }+9 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4081	23363	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4082	23398	\begin{align*} x^{2} y^{\prime \prime \prime \prime }-x y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
4083	24080	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.226
4084	24646	\begin{align*} 4 y+y^{\prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.226
4085	190	\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
4086	406	\begin{align*} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
4087	858	\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
4088	2681	\begin{align*} y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
4089	3158	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.227
4090	4560	\begin{align*} 2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.227
4091	5386	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
4092	5638	\begin{align*} {y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
4093	7887	\begin{align*} x \sqrt {y^{2}+x^{2}}-y+\left (y \sqrt {y^{2}+x^{2}}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
4094	9633	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
4095	10050	\begin{align*} y^{2} y^{\prime \prime }&=x \\ \end{align*}	✗	✓	✗	✗	0.227
4096	10358	\begin{align*} y^{\prime } x +y&=\tan \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.227
4097	10477	\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
4098	10609	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (4 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
4099	10729	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
4100	10770	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.227