2.3.42 Problems 4101 to 4200

Table 2.633: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4101	23361	\begin{align*} y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4102	1008	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.329
4103	1425	\begin{align*} x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.329
4104	7981	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4105	8763	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4106	9212	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4107	9229	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4108	10337	\begin{align*} y^{\prime } t +y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4109	14399	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.329
4110	14575	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4111	14640	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }&=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \\ \end{align*}	✓	✓	✓	✓	0.329
4112	22676	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4113	22690	\begin{align*} 4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4114	23096	\begin{align*} 4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right ) \\ 4 x+2 x^{\prime }+3 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.329
4115	23110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4116	23327	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4117	23642	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4118	23804	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.329
4119	922	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	0.330
4120	963	\begin{align*} x_{1}^{\prime }&=6 x_{1} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.330
4121	10334	\begin{align*} y^{\prime } t +y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.330
4122	15310	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.330
4123	17742	\begin{align*} 15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4124	23420	\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4125	23609	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.330
4126	23803	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.330
4127	3789	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=8 x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.331
4128	8633	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (4\right ) &= -3 \\ y^{\prime }\left (4\right ) &= -17 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4129	9610	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4130	10003	\begin{align*} \frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4131	10655	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4132	10706	\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4133	10926	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4134	11195	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4135	15695	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4136	16833	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.331
4137	19630	\begin{align*} y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✗	0.331
4138	26364	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.331
4139	625	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
4140	652	\begin{align*} y^{\prime }&=\left (x -2\right )^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.332
4141	1375	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4142	1416	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
4143	6152	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4144	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 \(x=0\).	✓	✓	✓	✓	0.332
4145	8128	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4146	10654	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4147	15207	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4148	16021	\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
4149	16728	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4150	17649	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
4151	22049	\begin{align*} 2 y x +y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4152	22109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4153	23357	\begin{align*} y^{\prime \prime }+9 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4154	23802	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.332
4155	25997	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4156	578	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.333
4157	1288	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.333
4158	2228	\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=x^{3} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.333
4159	2546	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
4160	7840	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4161	10570	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
4162	14576	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
4163	14800	\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.333
4164	16838	\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4165	19865	\begin{align*} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	0.333
4166	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*}	✓	✓	✓	✓	0.333
4167	23448	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4168	23766	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.333
4169	293	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.334
4170	465	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.334
4171	867	\begin{align*} 2 x^{\prime \prime }+16 x^{\prime }+40 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.334
4172	1366	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.334
4173	10335	\begin{align*} y^{\prime } t +y&=0 \\ y \left (0\right ) &= y_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	0.334
4174	10766	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4175	11025	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4176	15508	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4177	23031	\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4178	23318	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4179	23328	\begin{align*} 2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4180	23444	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.334
4181	23683	\begin{align*} x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.334
4182	333	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
4183	871	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
4184	1066	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
4185	1092	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
4186	1096	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
4187	1371	\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
4188	1419	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.335
4189	10948	\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
4190	13167	\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.335
4191	16460	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.335
4192	16716	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4193	19021	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.335
4194	23029	\begin{align*} x^{\prime \prime }-2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4195	23660	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.335
4196	23973	\begin{align*} y^{\prime \prime }-5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4197	25329	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.335
4198	2227	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=4 x \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 4 \\ y^{\prime \prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.336
4199	3922	\begin{align*} x_{1}^{\prime }&=-4 x_{1} \\ x_{2}^{\prime }&=-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.336
4200	3935	\begin{align*} y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336