2.3.22 Problems 2101 to 2200

Table 2.617: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2101	26848	\begin{align*} x^{\prime }+2 y&=3 t \\ y^{\prime }-2 x&=4 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.184
2102	27045	\begin{align*} 3 x^{\prime }-y&=2 t \\ x^{\prime }+y^{\prime }-y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.184
2103	1485	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.185
2104	4008	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.185
2105	10898	\begin{align*} 2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.185
2106	11186	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
2107	11297	\begin{align*} y^{\prime \prime }&=-\frac {y}{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.185
2108	17587	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.185
2109	18219	\begin{align*} y^{\prime \prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.185
2110	27735	\begin{align*} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{4 x} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.185
2111	6614	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
2112	10576	\begin{align*} 28 x^{2} \left (-3 x +1\right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
2113	10836	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
2114	11251	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
2115	16576	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
2116	17364	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
2117	17583	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.186
2118	17601	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.186
2119	24055	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.186
2120	26845	\begin{align*} x^{\prime }+y&=0 \\ x+y^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.186
2121	27738	\begin{align*} x y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
2122	359	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.187
2123	362	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\cos \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.187
2124	4474	\begin{align*} y^{\prime \prime \prime \prime }-y&=4 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.187
2125	10554	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
2126	10781	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
2127	10899	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.187
2128	15692	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.187
2129	15711	\begin{align*} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.187
2130	16956	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.187
2131	17758	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.187
2132	22641	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }-16 y^{\prime \prime }+12 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
2133	23394	\begin{align*} x^{6} y^{\left (6\right )}-12 x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
2134	23999	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.187
2135	24634	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.187
2136	343	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&={\mathrm e}^{x}+2 x^{2}-5 \\ \end{align*}	✓	✓	✓	✓	0.188
2137	360	\begin{align*} y^{\prime \prime \prime \prime }-y&=5 \\ 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 ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.188
2138	2111	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= k_{0} \\ y^{\prime }\left (1\right ) &= k_{1} \\ y^{\prime \prime }\left (1\right ) &= k_{2} \\ \end{align*}	✓	✓	✓	✓	0.188
2139	2149	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.188
2140	2150	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \\ \end{align*}	✓	✓	✓	✓	0.188
2141	3212	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.188
2142	6623	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
2143	10577	\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.188
2144	17366	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
2145	25259	\begin{align*} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.188
2146	26851	\begin{align*} x^{\prime }&=y-z \\ y^{\prime }&=x+y \\ z^{\prime }&=x+z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.188
2147	27017	\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.188
2148	255	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 14 \\ y^{\prime \prime }\left (1\right ) &= 22 \\ \end{align*}	✓	✓	✓	✓	0.189
2149	541	\begin{align*} x^{\prime \prime }+6 x^{\prime }+25 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.189
2150	3193	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.189
2151	6733	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.189
2152	10994	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.189
2153	15714	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.189
2154	16755	\begin{align*} y^{\left (6\right )}-64 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.189
2155	20352	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y&=\cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.189
2156	22151	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.189
2157	24664	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=36 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.189
2158	25257	\begin{align*} y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.189
2159	27693	\begin{align*} x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.189
2160	270	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
2161	556	\begin{align*} t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.190
2162	559	\begin{align*} t x^{\prime \prime }-2 x^{\prime }+x t&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.190
2163	2172	\begin{align*} 2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (11+12 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.190
2164	3799	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=\sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.190
2165	6649	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
2166	10575	\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
2167	10616	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
2168	10825	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
2169	11171	\begin{align*} x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
2170	11172	\begin{align*} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
2171	12712	\begin{align*} y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
2172	17569	\begin{align*} 8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -14 \\ y^{\prime \prime }\left (0\right ) &= -14 \\ y^{\prime \prime \prime }\left (0\right ) &= 139 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= -{\frac {29}{4}} \\ \end{align*}	✓	✓	✓	✓	0.190
2173	18190	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.190
2174	19038	\begin{align*} x_{1}^{\prime }&=x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.190
2175	26847	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=2 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.190
2176	26853	\begin{align*} x^{\prime }+2 y^{\prime }+x+y+z&=0 \\ x^{\prime }+y^{\prime }+x+z&=0 \\ z^{\prime }+2 y^{\prime }-y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.190
2177	256	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 5 \\ y^{\prime \prime }\left (1\right ) &= -11 \\ \end{align*}	✓	✓	✓	✓	0.191
2178	6746	\begin{align*} y a^{2} b^{2}+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
2179	10852	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
2180	15693	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.191
2181	15694	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
2182	15695	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
2183	19975	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
2184	27615	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
2185	2167	\begin{align*} 2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y&=3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.192
2186	2208	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \\ \end{align*}	✓	✓	✓	✓	0.192
2187	6624	\begin{align*} y+y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2188	6734	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2189	6747	\begin{align*} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.192
2190	6755	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2191	6780	\begin{align*} -b^{4} x^{\frac {2}{a}} y+16 \left (1-2 a \right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (1-2 a \right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.192
2192	10679	\begin{align*} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2193	10829	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2194	10896	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2195	10903	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2196	10905	\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2197	11259	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2198	13182	\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.192
2199	14613	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.192
2200	15713	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2} \\ y \left (0\right ) &= {\frac {11}{4}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.192