2.3.47 Problems 4601 to 4700

Table 2.667: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4601	17371	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.323
4602	17580	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.323
4603	20130	\begin{align*} x^{2} y^{\prime \prime \prime }-4 y^{\prime \prime } x +6 y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.323
4604	21558	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.323
4605	21948	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.323
4606	22280	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.323
4607	22684	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.323
4608	25165	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.323
4609	27015	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.323
4610	1758	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.324
4611	3285	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.324
4612	3791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.324
4613	8565	\begin{align*} \left (2+x \right ) y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.324
4614	10142	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.324
4615	10883	\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.324
4616	18796	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.324
4617	19660	\begin{align*} x^{\prime }&=b \,{\mathrm e}^{t} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.324
4618	21857	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.324
4619	22676	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.324
4620	23380	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.324
4621	24700	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.324
4622	4177	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.325
4623	7589	\begin{align*} z^{\prime \prime }+z^{\prime }-z&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4624	7900	\begin{align*} y-\ln \left (x \right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4625	8070	\begin{align*} y^{\prime }&=2 x^{2}+3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.325
4626	8584	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.325
4627	9223	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4628	9572	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4629	10956	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.325
4630	15221	\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.325
4631	18344	\begin{align*} x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4632	21133	\begin{align*} x^{\prime \prime }+x&=3 t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.325
4633	21219	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.325
4634	22336	\begin{align*} {| y^{\prime }|}+1&=0 \\ \end{align*}	✗	✓	✗	✗	0.325
4635	22657	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4636	23999	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.325
4637	26481	\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.325
4638	27786	\begin{align*} y^{\prime } x&=x^{2} \mu +\ln \left (y\right ) \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.325
4639	423	\begin{align*} y^{\prime \prime }&=y^{\prime }+y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4640	1085	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.326
4641	6550	\begin{align*} x y^{2} y^{\prime \prime }&=a \\ \end{align*}	✗	✓	✓	✗	0.326
4642	7200	\begin{align*} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4643	7591	\begin{align*} y^{\prime \prime }-y^{\prime }-11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4644	8027	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }&=x +\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.326
4645	9615	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4646	9741	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4647	10479	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4648	10581	\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4649	10606	\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4650	10676	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4651	10703	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4652	10897	\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4653	15207	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4654	15711	\begin{align*} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4655	19468	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4656	21132	\begin{align*} x^{\prime \prime }+x&=t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	0.326
4657	21920	\begin{align*} y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4658	23419	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4659	24010	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.326
4660	25134	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.326
4661	3686	\begin{align*} 2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4662	8088	\begin{align*} z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.327
4663	9044	\begin{align*} y_{1}^{\prime }&=y_{1} \\ 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 ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.327
4664	10862	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.327
4665	14800	\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.327
4666	15416	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4667	18772	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4668	18959	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.327
4669	21145	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{k t} \\ \end{align*}	✓	✓	✓	✓	0.327
4670	21638	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.327
4671	24686	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 x^{3}-9 x^{2}+2 x -16 \\ \end{align*}	✓	✓	✓	✓	0.327
4672	432	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.328
4673	3498	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \\ \end{align*}	✓	✓	✓	✓	0.328
4674	8574	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.328
4675	9467	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.328
4676	10343	\begin{align*} \left (a t +1\right ) y^{\prime }+y&=t \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.328
4677	10556	\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
4678	11223	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
4679	13072	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{2 t}+t \\ x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\ \end{align*}	✓	✓	✓	✗	0.328
4680	13788	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (\nu ^{2}+x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4681	14376	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.328
4682	16032	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4683	16489	\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4684	17410	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4685	19641	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.328
4686	20749	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4687	21214	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.328
4688	22480	\begin{align*} 2 y^{\prime \prime \prime \prime }&={\mathrm e}^{x}-{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.328
4689	23313	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4690	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*}	✓	✓	✓	✓	0.328
4691	23410	\begin{align*} x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
4692	24437	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.328
4693	24596	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.328
4694	24646	\begin{align*} 4 y+y^{\prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.328
4695	24660	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.328
4696	24933	\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.328
4697	27787	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=3 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.328
4698	427	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4699	568	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=2 \delta \left (t -\pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4700	1326	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329