2.3.57 Problems 5601 to 5700

Table 2.687: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5601	27581	\begin{align*} y^{\prime \prime }&=\left (2 y x -\frac {5}{x}\right ) y^{\prime }+4 y^{2}-\frac {4 y}{x^{2}} \\ \end{align*}	✗	✓	✓	✗	0.437
5602	27787	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=3 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.437
5603	1317	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.438
5604	2269	\begin{align*} y_{1}^{\prime }&=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }&=-3 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.438
5605	2367	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.438
5606	6697	\begin{align*} -8 y+3 x y^{\prime }+x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.438
5607	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*}	✓	✓	✓	✓	0.438
5608	8068	\begin{align*} x y^{\prime }&=1-x +2 y \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.438
5609	8891	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.438
5610	15188	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.438
5611	16188	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.438
5612	16190	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.438
5613	16829	\begin{align*} \left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.438
5614	16938	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.438
5615	17722	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.438
5616	19248	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.438
5617	19645	\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}	✓	✓	✓	✓	0.438
5618	24430	\begin{align*} y^{\prime \prime }-4 a y^{\prime }+3 a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.438
5619	25541	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.438
5620	26245	\begin{align*} \tan \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.438
5621	6700	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.439
5622	7522	\begin{align*} y^{\prime }&=-4 x-y \\ x^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.439
5623	7572	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.439
5624	15723	\begin{align*} y^{\prime }+3 y&=\delta \left (x -2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.439
5625	15770	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.439
5626	16832	\begin{align*} -2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.439
5627	19555	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.439
5628	26970	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.439
5629	622	\begin{align*} x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.440
5630	625	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.440
5631	1288	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.440
5632	2675	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{3} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.440
5633	7993	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.440
5634	8930	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.440
5635	17642	\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y&=\frac {1}{x^{13}} \\ \end{align*}	✓	✓	✓	✓	0.440
5636	17762	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.440
5637	17901	\begin{align*} \tan \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.440
5638	17993	\begin{align*} {y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.440
5639	19034	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.440
5640	22228	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.440
5641	23011	\begin{align*} 38 x^{\prime \prime }+10 x^{\prime }-3 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.440
5642	24774	\begin{align*} {y^{\prime }}^{2} x^{2}+x y^{\prime }-y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.440
5643	25670	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.440
5644	26491	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.440
5645	27148	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.440
5646	5	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {x +2}} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.441
5647	137	\begin{align*} 3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.441
5648	967	\begin{align*} x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.441
5649	3690	\begin{align*} \frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
5650	8610	\begin{align*} y^{\prime \prime }+k^{2} x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.441
5651	8716	\begin{align*} {y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
5652	9223	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
5653	16006	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.441
5654	16072	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.441
5655	16074	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.441
5656	16182	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.441
5657	16523	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 31 \\ \end{align*}	✓	✓	✓	✓	0.441
5658	16822	\begin{align*} y^{\prime }+\frac {2 y}{2 x -1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.441
5659	17392	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
5660	17821	\begin{align*} x^{\prime }&=6 \\ y^{\prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.441
5661	19514	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.441
5662	23040	\begin{align*} x^{\prime \prime }+9 x^{\prime }+8 x&=\sin \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.441
5663	26959	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\left (\alpha ^{2}-\epsilon ^{2}\right ) y&=0 \\ y \left (0\right ) &= c \\ y^{\prime }\left (0\right ) &= d \\ \end{align*}	✓	✓	✓	✓	0.441
5664	3187	\begin{align*} 4 y+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.442
5665	9114	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.442
5666	10588	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.442
5667	22793	\begin{align*} y^{\left (5\right )}-5 y^{\prime \prime }+4 y^{\prime }&=x^{2}-x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.442
5668	23073	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }-y&=7 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.442
5669	26933	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=-{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.442
5670	27588	\begin{align*} y y^{\prime }+2 x^{2} y^{\prime \prime }&={y^{\prime }}^{2} x \\ \end{align*}	✗	✓	✓	✗	0.442
5671	27755	\begin{align*} y^{\prime }&=y+x \,{\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.442
5672	815	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.443
5673	1863	\begin{align*} y^{\prime \prime }+2 x y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.443
5674	11731	\begin{align*} {y^{\prime }}^{2} x^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.443
5675	16594	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.443
5676	18780	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.443
5677	19637	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.443
5678	21120	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=0 \\ x \left (0\right ) &= a \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.443
5679	21190	\begin{align*} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.443
5680	25074	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=150 t \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.443
5681	25638	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.443
5682	26929	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.443
5683	465	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
5684	1261	\begin{align*} y^{\prime \prime }+5 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.444
5685	2801	\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.444
5686	3116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.444
5687	3209	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
5688	3931	\begin{align*} -y+y^{\prime }&=6 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.444
5689	4369	\begin{align*} \left (1+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \\ \end{align*}	✓	✓	✓	✓	0.444
5690	5760	\begin{align*} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
5691	7302	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x}+6 x -5 \\ \end{align*}	✓	✓	✓	✓	0.444
5692	7782	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
5693	9063	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.444
5694	9219	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
5695	12920	\begin{align*} y y^{\prime \prime }+y^{2}-a x -b&=0 \\ \end{align*}	✗	✗	✓	✗	0.444
5696	13779	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
5697	15979	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.444
5698	15987	\begin{align*} x^{\prime }&=-5 x-2 y \\ y^{\prime }&=-x-4 y \\ \end{align*}	✓	✓	✓	✓	0.444
5699	16071	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.444
5700	17393	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.444