2.3.57 Problems 5601 to 5700

Table 2.657: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5601	1714	\begin{align*} 2 y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5602	1867	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.365
5603	3927	\begin{align*} -2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.365
5604	4589	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.365
5605	6155	\begin{align*} \left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5606	6938	\begin{align*} {\mathrm e}^{x}-\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5607	8796	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.365
5608	9355	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.365
5609	14948	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.365
5610	16028	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.365
5611	16367	\begin{align*} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5612	16781	\begin{align*} y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.365
5613	17022	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.365
5614	17650	\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.365
5615	18253	\begin{align*} y^{\prime \prime }+y^{\prime }+y+1&=\sin \left (x \right )+x +x^{2} \\ \end{align*}	✓	✓	✓	✓	0.365
5616	18688	\begin{align*} x^{\prime }&=-x-\frac {y}{2} \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.365
5617	19208	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.365
5618	19583	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.365
5619	19775	\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5620	19865	\begin{align*} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	0.365
5621	20089	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=20 x \\ \end{align*}	✓	✓	✓	✓	0.365
5622	20792	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.365
5623	21959	\begin{align*} {y^{\prime \prime }}^{{3}/{2}}+y&=x \\ \end{align*}	✗	✓	✓	✗	0.365
5624	23031	\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5625	25112	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.365
5626	25331	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.365
5627	26074	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.365
5628	466	\begin{align*} \left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
5629	1776	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5630	1862	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
5631	2253	\begin{align*} y_{1}^{\prime }&=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-y_{1}+7 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.366
5632	3178	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.366
5633	3926	\begin{align*} x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.366
5634	5797	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5635	7728	\begin{align*} y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.366
5636	9063	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.366
5637	13062	\begin{align*} x^{\prime }&=a x-y \\ y^{\prime }&=x+a y \\ \end{align*}	✓	✓	✓	✓	0.366
5638	15272	\begin{align*} x^{\prime }+y^{\prime }&=y \\ x^{\prime }-y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.366
5639	16641	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.366
5640	16765	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.366
5641	18326	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.366
5642	18410	\begin{align*} x^{\prime }&=-9 y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.366
5643	18693	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.366
5644	19732	\begin{align*} y^{\prime }&={\mathrm e}^{z -y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	0.366
5645	21938	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5646	23030	\begin{align*} z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5647	25229	\begin{align*} t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
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*}	✓	✓	✓	✓	0.367
5649	5497	\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.367
5650	5997	\begin{align*} \left (a^{2} x^{2}+2\right ) y-2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.367
5651	19552	\begin{align*} y^{\prime \prime }-y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.367
5652	24585	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.367
5653	24598	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.367
5654	25616	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.367
5655	25934	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{3}+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.367
5656	143	\begin{align*} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
5657	507	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
5658	980	\begin{align*} x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.368
5659	1424	\begin{align*} x_{1}^{\prime }&=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.368
5660	3894	\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.368
5661	6236	\begin{align*} a^{2} y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5662	6472	\begin{align*} 2 y y^{\prime \prime }&=4 y^{2} \left (x +2 y\right )+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.368
5663	6948	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
5664	8489	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
5665	8816	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.368
5666	12917	\begin{align*} y y^{\prime \prime }-a x&=0 \\ \end{align*}	✗	✗	✗	✗	0.368
5667	14009	\begin{align*} x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5668	15971	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5669	15980	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.368
5670	16633	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=4 x \,{\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✓	0.368
5671	17361	\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5672	18431	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.368
5673	18652	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.368
5674	20775	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
5675	21648	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
5676	1930	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
5677	2196	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.369
5678	3987	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
5679	6179	\begin{align*} -\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5680	6684	\begin{align*} 6 n y^{\prime }-2 \left (n +1\right ) x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
5681	7804	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=\frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.369
5682	8484	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
5683	9634	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.369
5684	16982	\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ \end{align*}	✓	✓	✓	✓	0.369
5685	19512	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.369
5686	19566	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.369
5687	19626	\begin{align*} y^{\prime \prime }+y^{\prime }&=3 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.369
5688	20045	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.369
5689	21117	\begin{align*} x^{\prime \prime }+b x^{\prime }+c x&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5690	21270	\begin{align*} x^{\prime \prime }+t x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.369
5691	21297	\begin{align*} x^{\prime }&=-x+4 y \\ y^{\prime }&=3 x-5 y \\ \end{align*}	✓	✓	✓	✗	0.369
5692	22254	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.369
5693	24643	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
5694	25132	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.369
5695	4129	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.370
5696	6770	\begin{align*} \left (a +x \right )^{2} y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.370
5697	8815	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.370
5698	9367	\begin{align*} y^{\prime }&=1+y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.370
5699	9450	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.370
5700	12840	\begin{align*} y^{\prime \prime }-2 y^{3}-y x +a&=0 \\ \end{align*}	✗	✗	✗	✗	0.370