2.3.24 Problems 2301 to 2400

Table 2.579: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2301	7718	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.142
2302	7881	\begin{align*} x^{2}-y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
2303	7909	\begin{align*} 2 y-x^{3}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
2304	9535	\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 \(x=0\).	✗	✗	✓	✗	0.142
2305	10494	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
2306	11233	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
2307	12840	\begin{align*} y^{\prime \prime }-2 y^{3}-y x +a&=0 \\ \end{align*}	✗	✗	✗	✗	0.142
2308	12849	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \\ \end{align*}	✗	✗	✗	✗	0.142
2309	15298	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
2310	16794	\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.142
2311	16804	\begin{align*} y^{\prime \prime }&=\delta \left (-1+t \right )-\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.142
2312	362	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\cos \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.143
2313	1484	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.143
2314	2157	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y&=2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.143
2315	3170	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.143
2316	5886	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
2317	7788	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.143
2318	18101	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
2319	22049	\begin{align*} 2 y x +y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
2320	533	\begin{align*} x^{\prime \prime }+8 x^{\prime }+15 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2321	538	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2322	1056	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.144
2323	3123	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=x^{2}+8 \\ \end{align*}	✓	✓	✓	✓	0.144
2324	3943	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2325	5478	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
2326	7213	\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
2327	11210	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
2328	11264	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
2329	12839	\begin{align*} y^{\prime \prime }+a y^{2}+b x +c&=0 \\ \end{align*}	✗	✗	✗	✗	0.144
2330	13181	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.144
2331	15222	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2} \\ y \left (0\right ) &= -12 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2332	16593	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.144
2333	17581	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.144
2334	17601	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.144
2335	18458	\begin{align*} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2336	18463	\begin{align*} x^{\prime \prime }&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2337	18903	\begin{align*} y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2338	22245	\begin{align*} y^{\prime \prime }-y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2339	22320	\begin{align*} y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\ y \left (0\right ) &= -4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.144
2340	23391	\begin{align*} x^{5} y^{\left (5\right )}-2 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
2341	23999	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.144
2342	24053	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2343	1057	\begin{align*} 2 y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.145
2344	1629	\begin{align*} y^{\prime }+y&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.145
2345	2153	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{-2 x} \left (1-15 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.145
2346	2210	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.145
2347	2671	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2348	3194	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&={\mathrm e}^{2 x} \left (x -3\right ) \\ \end{align*}	✓	✓	✓	✓	0.145
2349	3284	\begin{align*} 4 y^{2}&=x^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.145
2350	3944	\begin{align*} y^{\prime \prime }-y&=6 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2351	6945	\begin{align*} x^{2}+y \cos \left (x \right )+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
2352	11099	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
2353	12914	\begin{align*} \sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}}&=0 \\ \end{align*}	✗	✗	✗	✗	0.145
2354	14814	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2355	15128	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }&=2 x^{2}+3 \\ \end{align*}	✓	✓	✓	✗	0.145
2356	15204	\begin{align*} y^{\prime \prime }+6 y^{\prime }+34 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2357	15701	\begin{align*} y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2358	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.	✓	✓	✓	✓	0.145
2359	16793	\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2360	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.	✓	✓	✓	✓	0.145
2361	17602	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\ \end{align*}	✓	✓	✓	✓	0.145
2362	18002	\begin{align*} x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\ \end{align*}	✓	✓	✓	✓	0.145
2363	18175	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.145
2364	18754	\begin{align*} y^{\prime \prime } x -\left (x +n \right ) y^{\prime }+n y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
2365	20088	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.145
2366	21552	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.145
2367	23649	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2368	25070	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2369	3730	\begin{align*} y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }&=5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.146
2370	3945	\begin{align*} y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.146
2371	4462	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }&=x^{2}+x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.146
2372	6629	\begin{align*} 4 y+2 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.146
2373	7883	\begin{align*} x +y \cos \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
2374	10903	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2375	11260	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2376	16791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.146
2377	16801	\begin{align*} y^{\prime }&=3 \delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.146
2378	17587	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.146
2379	17758	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.146
2380	18182	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.146
2381	18471	\begin{align*} 2 x^{\prime \prime }-2 x^{\prime }&=\left (t +1\right ) {\mathrm e}^{t} \\ x \left (0\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.146
2382	18901	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.146
2383	22600	\begin{align*} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime \prime }+24 x \\ 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 \\ \end{align*}	✓	✓	✓	✗	0.146
2384	537	\begin{align*} x^{\prime \prime }+9 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
2385	543	\begin{align*} x^{\prime \prime }-4 x&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
2386	3157	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.147
2387	3589	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2388	3932	\begin{align*} -y+y^{\prime }&=5 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
2389	9114	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.147
2390	9713	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2391	10872	\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2392	10915	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.147
2393	11302	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2394	16784	\begin{align*} y^{\prime \prime }+4 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
2395	18028	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2396	20593	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.147
2397	22809	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
2398	23389	\begin{align*} 2 x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2399	23392	\begin{align*} 7 x^{4} y^{\prime \prime \prime \prime }-2 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2400	340	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.148