2.3.57 Problems 5601 to 5700

Table 2.645: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5601	14384	\begin{align*} x^{\prime }&=-2 x \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.293
5602	15939	\begin{align*} y^{\prime }&=t^{2} \left (t^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	0.293
5603	16594	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.293
5604	16805	\begin{align*} y^{\prime }+2 y&=4 \delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.293
5605	18381	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.293
5606	18822	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.293
5607	20763	\begin{align*} y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.293
5608	22686	\begin{align*} y^{\prime \prime }+y&=2 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.293
5609	24899	\begin{align*} x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.293
5610	25134	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.293
5611	1062	\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 \(x=0\).	✓	✓	✓	✓	0.294
5612	1632	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\frac {1}{\left (x^{2}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	0.294
5613	8196	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\ \end{align*}	✓	✓	✓	✗	0.294
5614	9319	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.294
5615	18658	\begin{align*} x^{\prime }&=3 x+6 y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.294
5616	19049	\begin{align*} x_{1}^{\prime }&=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.294
5617	19108	\begin{align*} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
5618	20048	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y&=X \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.294
5619	20467	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.294
5620	21487	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
5621	22098	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
5622	22777	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.294
5623	23067	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.294
5624	24667	\begin{align*} y^{\prime \prime }+16 y&=24 \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.294
5625	25592	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.294
5626	1548	\begin{align*} y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.295
5627	2371	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= v \\ \end{align*}	✓	✓	✓	✓	0.295
5628	3290	\begin{align*} y^{2} {y^{\prime }}^{2}+x y^{\prime } y-2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5629	3419	\begin{align*} y^{\prime }&=\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.295
5630	3509	\begin{align*} \left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.295
5631	6864	\begin{align*} 2 y^{\prime } y+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5632	7890	\begin{align*} 2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.295
5633	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*}	✓	✓	✓	✓	0.295
5634	8758	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.295
5635	8963	\begin{align*} y^{\prime \prime }+3 x^{2} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.295
5636	9330	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=2 x -1 \\ \end{align*}	✓	✓	✓	✓	0.295
5637	9501	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.295
5638	14582	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5639	15304	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5640	16827	\begin{align*} \left (1-x \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=5\).	✓	✓	✓	✓	0.295
5641	17022	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.295
5642	20445	\begin{align*} {y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 y x -2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y}&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5643	22200	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.295
5644	22835	\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.295
5645	23471	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.295
5646	23790	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.295
5647	24140	\begin{align*} x +\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5648	24591	\begin{align*} y^{\prime \prime }-y&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.295
5649	25602	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.295
5650	25766	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.295
5651	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*}	✓	✓	✓	✗	0.296
5652	526	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
5653	1370	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.296
5654	3406	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.296
5655	5796	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.296
5656	6375	\begin{align*} x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.296
5657	7381	\begin{align*} y^{\prime }&=4 y^{2}-3 y+1 \\ \end{align*}	✓	✓	✓	✓	0.296
5658	7825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.296
5659	8757	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
5660	9223	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
5661	9377	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.296
5662	9468	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.296
5663	9723	\begin{align*} x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
5664	10232	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.296
5665	10261	\begin{align*} y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.296
5666	10272	\begin{align*} c y^{\prime }&=a x \\ \end{align*}	✓	✓	✓	✓	0.296
5667	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*}	✓	✓	✓	✗	0.296
5668	10571	\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.296
5669	10603	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.296
5670	10765	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.296
5671	10951	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.296
5672	12413	\begin{align*} x^{2} y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.296
5673	15197	\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 ) &= \frac {\sqrt {2}}{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.296
5674	16062	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.296
5675	17900	\begin{align*} {\mathrm e}^{y^{\prime }}&=x \\ \end{align*}	✓	✓	✓	✓	0.296
5676	18689	\begin{align*} x^{\prime }&=2 x+\frac {y}{2} \\ y^{\prime }&=-\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.296
5677	18860	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.296
5678	19622	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.296
5679	22626	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.296
5680	23033	\begin{align*} y^{\prime \prime }-3 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.296
5681	23679	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +y p&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.296
5682	24883	\begin{align*} y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.296
5683	25243	\begin{align*} -t y^{\prime \prime }+\left (t -2\right ) y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.296
5684	426	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.297
5685	4177	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.297
5686	6391	\begin{align*} \left (a +1\right ) x y^{\prime }+x^{2} y^{\prime \prime }&=x^{k} f \left (x^{k} y, k y+y^{\prime } x \right ) \\ \end{align*}	✗	✗	✗	✗	0.297
5687	10751	\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.297
5688	12927	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-y f^{\prime \prime }\left (x \right )+f \left (x \right ) y^{3}-y^{4}&=0 \\ \end{align*}	✗	✗	✓	✗	0.297
5689	13169	\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.297
5690	16182	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.297
5691	18785	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.297
5692	19607	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.297
5693	22305	\begin{align*} x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.297
5694	22936	\begin{align*} x^{\prime }-2 x+3 y&=0 \\ -2 x+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.297
5695	23504	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.297
5696	23560	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.297
5697	23697	\begin{align*} \left (x^{2}+4 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y&=0 \\ y \left (-2\right ) &= 0 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.297
5698	24004	\begin{align*} y^{\prime \prime }-y&=4 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.297
5699	24573	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.297
5700	24661	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.297