2.3.44 Problems 4301 to 4400

Table 2.661: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4301	18395	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4302	21214	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.329
4303	21486	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4304	21731	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4305	23145	\begin{align*} y^{\prime } y&=x^{3} y^{2}+x y^{2} \\ \end{align*}	✓	✓	✓	✓	0.329
4306	24777	\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4307	25287	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.329
4308	25569	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.329
4309	3708	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4310	6304	\begin{align*} y^{\prime \prime }&=a +x y+2 y^{3} \\ \end{align*}	✗	✗	✗	✗	0.330
4311	6941	\begin{align*} 3 y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4312	10139	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.330
4313	10976	\begin{align*} x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4314	21541	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.330
4315	21714	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.330
4316	22513	\begin{align*} y^{\prime }+2 x&=2 \\ \end{align*}	✓	✓	✓	✓	0.330
4317	23010	\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4318	24505	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-4 y^{\prime \prime }-4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4319	25374	\begin{align*} y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.330
4320	26712	\begin{align*} y^{\prime \prime }&=x^{2} y-y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
4321	26763	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.330
4322	1274	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4323	7901	\begin{align*} 3 x^{2}+y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4324	10561	\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4325	14523	\begin{align*} y^{2} {\mathrm e}^{2 x}+\left (y \,{\mathrm e}^{2 x}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4326	15334	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4327	16968	\begin{align*} x^{\prime \prime }+2 x^{\prime }-10 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4328	18281	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.331
4329	20036	\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4330	20840	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4331	23426	\begin{align*} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4332	443	\begin{align*} y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.332
4333	1075	\begin{align*} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4334	1459	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.332
4335	2376	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4336	2546	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4337	2726	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=t^{3} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.332
4338	3284	\begin{align*} 4 y^{2}&={y^{\prime }}^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.332
4339	3617	\begin{align*} y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.332
4340	4005	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{1-x}+x y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4341	6749	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.332
4342	8099	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
4343	8932	\begin{align*} y^{\prime \prime }-2 i y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4344	10723	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4345	10756	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4346	10776	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4347	10883	\begin{align*} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4348	10959	\begin{align*} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4349	10971	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4350	11018	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4351	11080	\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4352	11082	\begin{align*} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4353	11267	\begin{align*} x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4354	12336	\begin{align*} y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
4355	14276	\begin{align*} x+3 t x^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4356	14296	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.332
4357	14431	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.332
4358	15210	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4359	19466	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4360	20386	\begin{align*} y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.332
4361	21109	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4362	22252	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.332
4363	24455	\begin{align*} 4 y^{\left (5\right )}-23 y^{\prime \prime \prime }-33 y^{\prime \prime }-17 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
4364	25592	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.332
4365	811	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.333
4366	812	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.333
4367	1062	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333
4368	1282	\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
4369	2174	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.333
4370	5412	\begin{align*} y^{\prime } y+{y^{\prime }}^{2}&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.333
4371	7912	\begin{align*} 3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
4372	10074	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.333
4373	10222	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.333
4374	11180	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
4375	15703	\begin{align*} y^{\prime \prime }-9 y&=x +2 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.333
4376	21727	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.333
4377	25121	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.333
4378	3061	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4379	7142	\begin{align*} x y y^{\prime \prime }-2 {y^{\prime }}^{2} x +\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.334
4380	7458	\begin{align*} \frac {t y^{\prime }}{y}+1+\ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4381	10565	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4382	10689	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4383	10711	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
4384	18081	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.334
4385	18212	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.334
4386	19474	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
4387	19640	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.334
4388	26067	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=-y_{1}+2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.334
4389	26932	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=15 \\ \end{align*}	✓	✓	✓	✓	0.334
4390	342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
4391	2316	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.335
4392	6616	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.335
4393	7621	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -{\frac {17}{2}} \\ \end{align*}	✓	✓	✓	✓	0.335
4394	7887	\begin{align*} x \sqrt {y^{2}+x^{2}}-y+\left (y \sqrt {y^{2}+x^{2}}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
4395	8142	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
4396	10242	\begin{align*} y+y^{\prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.335
4397	10794	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
4398	11130	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
4399	12798	\begin{align*} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
4400	15001	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=-5 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.335