2.3.23 Problems 2201 to 2300

Table 2.577: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2201	4491	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=10 \,{\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.135
2202	7942	\begin{align*} x^{2} {y^{\prime }}^{2}+x y^{\prime } y-6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
2203	8930	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.135
2204	10337	\begin{align*} t y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
2205	10348	\begin{align*} y^{\prime } x +y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✗	✗	0.135
2206	15202	\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
2207	17366	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
2208	17599	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.135
2209	18176	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.135
2210	18256	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x}+2 x \\ \end{align*}	✓	✓	✓	✓	0.135
2211	18470	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=4 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
2212	18962	\begin{align*} \frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
2213	20049	\begin{align*} y^{\prime \prime \prime }+y&=3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.135
2214	20195	\begin{align*} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.135
2215	25059	\begin{align*} y^{\prime }-4 y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
2216	459	\begin{align*} x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.136
2217	4466	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=48 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.136
2218	6300	\begin{align*} y^{\prime \prime }&=x +6 y^{2} \\ \end{align*}	✗	✗	✗	✗	0.136
2219	8531	\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.136
2220	9452	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.136
2221	9710	\begin{align*} -y^{2}+x^{2} {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
2222	10335	\begin{align*} t y^{\prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	0.136
2223	11251	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.136
2224	14948	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.136
2225	15315	\begin{align*} y^{\prime \prime } x +x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
2226	18089	\begin{align*} y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.136
2227	18276	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.136
2228	21180	\begin{align*} x^{\prime \prime \prime }+4 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ x^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.136
2229	22086	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +y&=4 x y^{2} \\ \end{align*}	✗	✗	✗	✗	0.136
2230	23487	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.136
2231	23641	\begin{align*} y^{\prime \prime }-9 y&=20 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 18 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.136
2232	6939	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.137
2233	9115	\begin{align*} y x +x^{2} y^{\prime }&=2 x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.137
2234	14099	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.137
2235	17536	\begin{align*} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.137
2236	17575	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.137
2237	18963	\begin{align*} \frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.137
2238	20072	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (m x \right ) \\ \end{align*}	✓	✓	✓	✓	0.137
2239	4472	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+5 y^{\prime }+5 y&=5 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.138
2240	5018	\begin{align*} x^{{3}/{2}} y^{\prime }&=a +b \,x^{{3}/{2}} y^{2} \\ \end{align*}	✓	✓	✓	✗	0.138
2241	5767	\begin{align*} y x -y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.138
2242	6603	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.138
2243	6670	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.138
2244	6778	\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*}	✓	✓	✓	✗	0.138
2245	8814	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.138
2246	11036	\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*}	✓	✓	✓	✗	0.138
2247	11121	\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.138
2248	11153	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.138
2249	13663	\begin{align*} y^{\prime \prime }-\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.138
2250	14697	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.138
2251	16775	\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.138
2252	16788	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.138
2253	17201	\begin{align*} 3 t y^{2}+y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.138
2254	17368	\begin{align*} y^{\prime \prime }+49 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.138
2255	23643	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.138
2256	6874	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
2257	7200	\begin{align*} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
2258	9307	\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}	✓	✓	✓	✓	0.139
2259	11249	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.139
2260	12910	\begin{align*} x^{4} y^{\prime \prime }+a^{2} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.139
2261	16778	\begin{align*} y^{\prime \prime }+8 y^{\prime }+17 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.139
2262	18889	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.139
2263	19829	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
2264	20070	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \left (b x +a \right ) \\ \end{align*}	✓	✓	✓	✓	0.139
2265	20749	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
2266	20866	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
2267	22788	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=12 \,{\mathrm e}^{2 x}+24 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.139
2268	6398	\begin{align*} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.140
2269	6944	\begin{align*} 2 y x +x^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.140
2270	14083	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
2271	14627	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.140
2272	14947	\begin{align*} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.140
2273	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.	✓	✓	✓	✓	0.140
2274	17598	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.140
2275	18174	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.140
2276	18312	\begin{align*} y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.140
2277	23631	\begin{align*} y^{\prime \prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.140
2278	24790	\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
2279	270	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
2280	1781	\begin{align*} 4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+\cos \left (x \right ) x \right ) y^{\prime }+\left (2 \cos \left (x \right ) x +3 \sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
2281	4516	\begin{align*} y^{\prime \prime }+4 y&=8 \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141
2282	7802	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.141
2283	7990	\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.141
2284	8634	\begin{align*} y^{\prime }-6 y&=0 \\ y \left (-1\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141
2285	8948	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.141
2286	9613	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141
2287	9712	\begin{align*} x^{2} {y^{\prime }}^{2}-5 x y^{\prime } y+6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
2288	10334	\begin{align*} t y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141
2289	11093	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
2290	11286	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
2291	15310	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.141
2292	15694	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141
2293	16443	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
2294	16783	\begin{align*} y^{\prime \prime }+4 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141
2295	17582	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.141
2296	20582	\begin{align*} n \,x^{3} y^{\prime \prime \prime }&=y-y^{\prime } x \\ \end{align*}	✓	✓	✓	✗	0.141
2297	3156	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.142
2298	3693	\begin{align*} y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
2299	5524	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
2300	6647	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \left (1-{\mathrm e}^{x} x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.142