2.3.42 Problems 4101 to 4200

Table 2.657: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4101	8028	\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.332
4102	8127	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4103	8893	\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4104	15128	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }&=2 x^{2}+3 \\ \end{align*}	✓	✓	✓	✗	0.332
4105	16025	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
4106	16721	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4107	16763	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4108	16782	\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.	✓	✓	✓	✓	0.332
4109	18468	\begin{align*} x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4110	21912	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4111	23703	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4112	23788	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.332
4113	23975	\begin{align*} y^{\prime \prime }-2 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4114	25098	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4115	442	\begin{align*} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4116	1062	\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 \(x=0\).	✓	✓	✓	✓	0.333
4117	1398	\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4118	1627	\begin{align*} x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\ \end{align*}	✓	✓	✓	✓	0.333
4119	1771	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=4 x^{{5}/{2}} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.333
4120	10568	\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*}	✓	✓	✓	✗	0.333
4121	11163	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.333
4122	14813	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
4123	16968	\begin{align*} x^{\prime \prime }+2 x^{\prime }-10 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
4124	24056	\begin{align*} y^{\left (5\right )}&=120 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 24 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
4125	2555	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4126	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*}	✓	✓	✓	✗	0.334
4127	10685	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4128	10937	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4129	16184	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ \end{align*}	✓	✓	✓	✓	0.334
4130	16460	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.334
4131	17380	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4132	19463	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4133	20334	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4134	276	\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4135	380	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
4136	1303	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4137	1765	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.335
4138	9079	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4139	10612	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
4140	11226	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
4141	15988	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+4 y \\ \end{align*}	✓	✓	✓	✓	0.335
4142	20454	\begin{align*} y&=x y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.335
4143	23662	\begin{align*} y^{\prime \prime \prime }+8 y&=-12 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= -8 \\ y^{\prime }\left (0\right ) &= 24 \\ y^{\prime \prime }\left (0\right ) &= -46 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.335
4144	23812	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-3 y \\ \end{align*}	✓	✓	✓	✓	0.335
4145	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.	✓	✓	✓	✓	0.335
4146	27091	\(\left [\begin {array}{cc} 6 & -2 \\ -3 & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.335
4147	419	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
4148	431	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
4149	1010	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.336
4150	1304	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4151	3789	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=8 x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.336
4152	7267	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4153	8109	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
4154	10252	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4155	16056	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.336
4156	17382	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4157	17383	\begin{align*} y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4158	18469	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=2 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4159	19981	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) x&=1 \\ \end{align*}	✓	✓	✓	✓	0.336
4160	20007	\begin{align*} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\ \end{align*}	✓	✓	✓	✓	0.336
4161	20746	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.336
4162	23028	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4163	23713	\begin{align*} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
4164	25535	\begin{align*} 2 y^{\prime \prime }+8 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4165	26132	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.336
4166	26488	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4167	26722	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4168	27757	\begin{align*} y^{\prime }&=x^{2}+y^{3} \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.336
4169	353	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.337
4170	1770	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=-{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.337
4171	3087	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4172	7585	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4173	9029	\begin{align*} 3 x^{2} \ln \left (x \right )+x^{2}+y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4174	11032	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
4175	11200	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
4176	14996	\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.337
4177	23398	\begin{align*} x^{2} y^{\prime \prime \prime \prime }-x y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4178	1008	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.338
4179	1759	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.338
4180	2418	\begin{align*} y^{\prime \prime }-t^{3} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.338
4181	3195	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.338
4182	7062	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4183	7588	\begin{align*} 6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4184	9109	\begin{align*} y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4185	10797	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4186	11062	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4187	13165	\(\left [\begin {array}{cc} 0 & -6 \\ 6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.338
4188	16262	\begin{align*} y^{\prime }-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4189	16853	\begin{align*} y^{\prime }+\cos \left (y\right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4190	17359	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4191	19475	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4192	26764	\begin{align*} x^{\prime }&=-x-y \\ y^{\prime }&=x-3 y \\ \end{align*}	✓	✓	✓	✓	0.338
4193	27730	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4194	1366	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4195	1378	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4196	1416	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.339
4197	2221	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=2 x \\ \end{align*}	✓	✓	✓	✓	0.339
4198	8630	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4199	9452	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4200	10350	\begin{align*} x y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.339