2.3.47 Problems 4601 to 4700

Table 2.637: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4601	21140	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.307
4602	23425	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.307
4603	24434	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.307
4604	24592	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.307
4605	2548	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.308
4606	3120	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.308
4607	3404	\begin{align*} y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\ \end{align*}	✓	✓	✓	✓	0.308
4608	6724	\begin{align*} \sin \left (x \right )-\cos \left (x \right ) y-3 \sin \left (x \right ) y^{\prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.308
4609	7200	\begin{align*} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.308
4610	8131	\begin{align*} y^{\prime \prime }-y x&=\frac {1}{1-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.308
4611	11067	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.308
4612	18234	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.308
4613	20933	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.308
4614	21530	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.308
4615	22232	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.308
4616	434	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.309
4617	446	\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.309
4618	815	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.309
4619	836	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4620	871	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.309
4621	1077	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.309
4622	1091	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.309
4623	1383	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.309
4624	1417	\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.309
4625	2376	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4626	6044	\begin{align*} \left (4 x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4627	8088	\begin{align*} z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.309
4628	8609	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.309
4629	10589	\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4630	10674	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4631	14570	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4632	15970	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.309
4633	18193	\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.309
4634	19435	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.309
4635	19439	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.309
4636	21527	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.309
4637	21876	\begin{align*} 9 y^{\prime \prime }-30 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4638	21952	\begin{align*} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\ \end{align*}	✗	✗	✗	✗	0.309
4639	22072	\begin{align*} y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.309
4640	23017	\begin{align*} y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4641	23334	\begin{align*} 8 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4642	24259	\begin{align*} \left (a +x \right ) y^{\prime }&=b x \\ \end{align*}	✓	✓	✓	✓	0.309
4643	879	\begin{align*} y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.310
4644	1334	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.310
4645	1367	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.310
4646	2558	\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4647	4122	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4648	5943	\begin{align*} -y x -\left (2 x^{2}+1\right ) y^{\prime }+2 y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.310
4649	5999	\begin{align*} \left (b \,x^{2}+a \right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4650	6013	\begin{align*} \left (-x^{2}+2\right ) y+4 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4651	8568	\begin{align*} y^{\prime } x -3 y&=k \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.310
4652	15332	\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.310
4653	15989	\begin{align*} x^{\prime }&=-\frac {x}{2} \\ y^{\prime }&=x-\frac {y}{2} \\ \end{align*}	✓	✓	✓	✓	0.310
4654	16496	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 19 \\ \end{align*}	✓	✓	✓	✓	0.310
4655	16814	\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.310
4656	17622	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4657	19438	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.310
4658	20911	\begin{align*} 2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.310
4659	23023	\begin{align*} x^{\prime \prime }+2 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi \sqrt {3}}{6}\right ) &= 2 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{6}} \\ \end{align*}	✓	✓	✓	✓	0.310
4660	26062	\begin{align*} -y^{\prime } x +y&={y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.310
4661	8	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.311
4662	225	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.311
4663	7905	\begin{align*} y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.311
4664	9618	\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.311
4665	18392	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.311
4666	19478	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.311
4667	20050	\begin{align*} y^{\prime \prime \prime }-y&=\left ({\mathrm e}^{x}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.311
4668	447	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ y \left (-3\right ) &= 0 \\ y^{\prime }\left (-3\right ) &= 2 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.312
4669	816	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 13 \\ \end{align*}	✓	✓	✓	✓	0.312
4670	3232	\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\ \end{align*}	✓	✓	✓	✓	0.312
4671	5898	\begin{align*} a x y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4672	6277	\begin{align*} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (-x +2\right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.312
4673	6961	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4674	9716	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4675	18201	\begin{align*} y^{\prime \prime }+4 y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.312
4676	18204	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.312
4677	20735	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\ \end{align*}	✓	✓	✓	✓	0.312
4678	20765	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3+7 x \right ) y^{\prime }-3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	0.312
4679	20889	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.312
4680	25073	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.312
4681	25102	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4682	540	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=6 x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	0.313
4683	652	\begin{align*} y^{\prime }&=\left (x -2\right )^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.313
4684	2378	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
4685	6165	\begin{align*} \left (x^{4}+2 x^{2}+a \right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
4686	6701	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.313
4687	8483	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.313
4688	8567	\begin{align*} y^{\prime }&=-2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.313
4689	9111	\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.313
4690	13187	\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.313
4691	15087	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=\frac {y y^{\prime }}{\sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	0.313
4692	15442	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.313
4693	15472	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.313
4694	16471	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -9 \\ \end{align*}	✓	✓	✓	✓	0.313
4695	20042	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
4696	20148	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.313
4697	20192	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
4698	21207	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.313
4699	21208	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.313
4700	23022	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi \sqrt {3}}{3}\right ) &= 5 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.313