2.3.47 Problems 4601 to 4700

Table 2.625: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4601	1311	\begin{align*} 25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.249
4602	1880	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.249
4603	5909	\begin{align*} b \,x^{k} y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
4604	6309	\begin{align*} a \,x^{r} y^{s}+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.249
4605	7142	\begin{align*} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.249
4606	9639	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right )+t \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.249
4607	10347	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.249
4608	10552	\begin{align*} 2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
4609	10640	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
4610	14817	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.249
4611	18955	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.249
4612	20007	\begin{align*} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\ \end{align*}	✓	✓	✓	✓	0.249
4613	22747	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.249
4614	23443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.249
4615	24439	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.249
4616	24542	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.249
4617	1308	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4618	1756	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.250
4619	1760	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=7 x^{{3}/{2}} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.250
4620	3285	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4621	3763	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.250
4622	3764	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.250
4623	3987	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4624	7165	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4625	8074	\begin{align*} y^{\prime \prime }-y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4626	8567	\begin{align*} y^{\prime }&=-2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4627	8681	\begin{align*} x^{\prime }+t&=1 \\ \end{align*}	✓	✓	✓	✓	0.250
4628	8832	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
4629	8962	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4630	10346	\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4631	10517	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
4632	10634	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
4633	10665	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4634	10698	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
4635	10935	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
4636	11026	\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*}	✓	✓	✓	✗	0.250
4637	13142	\(\left [\begin {array}{cc} 10 & -9 \\ 6 & -5 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.250
4638	13143	\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.250
4639	15497	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4640	16258	\begin{align*} y^{\prime }-x y^{2}&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✗	0.250
4641	16513	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4642	17410	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4643	18772	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4644	18944	\begin{align*} y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.250
4645	19185	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4646	20416	\begin{align*} y&=y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	0.250
4647	20538	\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.250
4648	20761	\begin{align*} \left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
4649	23250	\begin{align*} 2 y-3 y^{\prime \prime } x +4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4650	23318	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4651	23450	\begin{align*} y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.250
4652	24599	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.250
4653	24699	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x -2\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.250
4654	25095	\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
4655	25174	\begin{align*} y_{1}^{\prime }&=-y_{2} \\ y_{2}^{\prime }-2 y_{2}&=y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.250
4656	25586	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.250
4657	7	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.251
4658	1361	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.251
4659	2365	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4660	7064	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4661	9170	\begin{align*} y^{\prime } x +y+3 x^{3} y^{4} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4662	9607	\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.251
4663	10866	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
4664	10952	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
4665	10981	\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
4666	13147	\(\left [\begin {array}{cc} 9 & -10 \\ 2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.251
4667	14580	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4668	16503	\begin{align*} 25 y^{\prime \prime }-10 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4669	16505	\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4670	16822	\begin{align*} y^{\prime }+\frac {2 y}{2 x -1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.251
4671	17008	\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+153 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4672	21482	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
4673	23788	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.251
4674	24546	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \cos \left (x \right )+4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.251
4675	24588	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.251
4676	24623	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.251
4677	420	\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 \(x=0\).	✓	✓	✓	✓	0.252
4678	428	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.252
4679	430	\begin{align*} \left (x^{2}-3\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.252
4680	1306	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4681	1743	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4682	5479	\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4683	6449	\begin{align*} y y^{\prime \prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.252
4684	6597	\begin{align*} f \left (y^{\prime \prime }\right )+y^{\prime \prime } x&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.252
4685	7905	\begin{align*} y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
4686	10685	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
4687	11167	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.252
4688	14060	\begin{align*} \left (-y+y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.252
4689	14771	\begin{align*} x^{\prime }+y^{\prime }-2 x-4 y&={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✗	0.252
4690	14800	\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.252
4691	16500	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4692	16502	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4693	17338	\begin{align*} y-t y^{\prime }&=-4 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.252
4694	21191	\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.252
4695	22622	\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4696	22657	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.252
4697	22688	\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.252
4698	24597	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=4-{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.252
4699	25617	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.252
4700	10	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.253