2.3.23 Problems 2201 to 2300

Table 2.595: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2201	14708	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
2202	16792	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.190
2203	16799	\begin{align*} y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.190
2204	20806	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.190
2205	22233	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 t^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.190
2206	24526	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.190
2207	24556	\begin{align*} y^{\prime \prime \prime \prime }-y&=7 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.190
2208	2672	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
2209	3157	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.191
2210	7327	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
2211	8814	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.191
2212	10965	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
2213	16801	\begin{align*} y^{\prime }&=3 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
2214	17598	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.191
2215	17602	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\ \end{align*}	✓	✓	✓	✓	0.191
2216	20085	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \,{\mathrm e}^{x}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.191
2217	22263	\begin{align*} w^{\prime }-y&=0 \\ w+y^{\prime }+z&=1 \\ w-y+z^{\prime }&=2 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ w \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.191
2218	24610	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.191
2219	25286	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✓	0.191
2220	551	\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=t \,{\mathrm e}^{-t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.192
2221	5966	\begin{align*} -\left (a \left (-1+a \right )-b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2222	11284	\begin{align*} y^{\prime \prime }&=\frac {12 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.192
2223	12812	\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2224	17601	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.192
2225	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*}	✓	✓	✓	✓	0.192
2226	24525	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.192
2227	25636	\begin{align*} y^{\prime }-a y&=t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.192
2228	26104	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.192
2229	546	\begin{align*} x^{\prime \prime \prime \prime }-x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.193
2230	1252	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
2231	3798	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.193
2232	8165	\begin{align*} \left (-x +y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	0.193
2233	8924	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.193
2234	9106	\begin{align*} y^{\prime } x -3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.193
2235	11083	\begin{align*} 2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
2236	11286	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2237	14565	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
2238	16767	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=7 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.193
2239	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*}	✓	✓	✓	✓	0.193
2240	25630	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.193
2241	440	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.194
2242	857	\begin{align*} y^{\prime \prime }-2 i y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2243	2175	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.194
2244	8507	\begin{align*} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.194
2245	8978	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2246	10300	\begin{align*} x y \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2247	10554	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2248	10834	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2249	10898	\begin{align*} 2 y^{\prime \prime } x +\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2250	11186	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2251	12785	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2252	16817	\begin{align*} y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2253	18753	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2254	19608	\begin{align*} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.194
2255	20070	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \left (b x +a \right ) \\ \end{align*}	✓	✓	✓	✓	0.194
2256	22691	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.194
2257	23019	\begin{align*} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.194
2258	24001	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x -{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.194
2259	24527	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+14 y^{\prime }-8 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.194
2260	24529	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.194
2261	25082	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2262	25996	\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.	✓	✓	✓	✓	0.194
2263	3765	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.195
2264	10820	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2265	11208	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2266	17583	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.195
2267	17761	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.195
2268	20094	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2269	20195	\begin{align*} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2270	25080	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.195
2271	25084	\begin{align*} y^{\prime \prime }-3 y&=4 t^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.195
2272	26440	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.195
2273	1487	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.196
2274	7073	\begin{align*} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.196
2275	7330	\begin{align*} x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2276	10829	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2277	10852	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
2278	18088	\begin{align*} y^{\prime \prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.196
2279	23511	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.196
2280	25244	\begin{align*} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.196
2281	25640	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.196
2282	439	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.197
2283	6695	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2284	6700	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2285	6702	\begin{align*} 2 y-2 y^{\prime } x +3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2286	6705	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2287	10557	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2288	11249	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2289	11251	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2290	13182	\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.197
2291	13183	\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.197
2292	13934	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2293	16774	\begin{align*} y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
2294	18219	\begin{align*} y^{\prime \prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.197
2295	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.197
2296	22173	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.197
2297	22240	\begin{align*} y^{\prime }+2 y&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
2298	24480	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }-11 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2299	24528	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.197
2300	25632	\begin{align*} y^{\prime \prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197