2.3.77 Problems 7601 to 7700

Table 2.697: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7601	16948	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*}	✓	✓	✓	✓	0.489
7602	19163	\begin{align*} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } x -y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.489
7603	19511	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.489
7604	19878	\begin{align*} V^{\prime \prime }+\frac {2 V^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.489
7605	25660	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.489
7606	979	\begin{align*} x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.490
7607	2375	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.490
7608	3248	\begin{align*} y^{\prime \prime } x&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.490
7609	8277	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.490
7610	11682	\begin{align*} {y^{\prime }}^{2}+\left (a y+b x \right ) y^{\prime }+a b x y&=0 \\ \end{align*}	✓	✓	✓	✓	0.490
7611	12905	\begin{align*} 2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.490
7612	14799	\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.490
7613	15007	\begin{align*} x^{\prime }&=-11 x-2 y \\ y^{\prime }&=13 x-9 y \\ \end{align*}	✓	✓	✓	✓	0.490
7614	16030	\begin{align*} x^{\prime }&=2 x+4 y \\ y^{\prime }&=3 x+6 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.490
7615	17807	\begin{align*} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.490
7616	19171	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.490
7617	19654	\begin{align*} x^{\prime }&=5 x+2 y \\ y^{\prime }&=-17 x-5 y \\ \end{align*}	✓	✓	✓	✓	0.490
7618	20604	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.490
7619	21546	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.490
7620	157	\begin{align*} y^{\prime \prime }&=2 y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.491
7621	1910	\begin{align*} \left (3 x +2\right ) y^{\prime \prime }-y^{\prime } x +2 y x&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.491
7622	2414	\begin{align*} \left (t^{2}+2\right ) y^{\prime \prime }-y^{\prime } t -3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.491
7623	2681	\begin{align*} y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.491
7624	2718	\begin{align*} y^{\prime \prime \prime \prime }-y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.491
7625	3571	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.491
7626	6523	\begin{align*} 2 x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.491
7627	8938	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.491
7628	9720	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.491
7629	15268	\begin{align*} x^{\prime }+5 x-2 y&=0 \\ 2 x+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.491
7630	15982	\begin{align*} x^{\prime }&=-2 x-3 y \\ y^{\prime }&=3 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.491
7631	16090	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.491
7632	17526	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=65 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.491
7633	19245	\begin{align*} \left (x +1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.491
7634	20018	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.491
7635	23042	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.491
7636	24573	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.491
7637	4	\begin{align*} y^{\prime }&=\frac {1}{x^{2}} \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.492
7638	3745	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.492
7639	4374	\begin{align*} 3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.492
7640	6103	\begin{align*} -2 y+2 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.492
7641	7344	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=26 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.492
7642	7496	\begin{align*} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.492
7643	10353	\begin{align*} y^{\prime } x +y&=\frac {1}{x^{3}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.492
7644	14088	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.492
7645	19521	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.492
7646	21002	\begin{align*} z^{2} u^{\prime \prime }+\left (3 z +1\right ) u^{\prime }+u&=0 \\ \end{align*}	✓	✓	✓	✗	0.492
7647	21684	\begin{align*} x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.492
7648	22749	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.492
7649	24898	\begin{align*} x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.492
7650	25124	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 t \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.492
7651	190	\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.493
7652	977	\begin{align*} x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.493
7653	1025	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.493
7654	3725	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.493
7655	5647	\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.493
7656	6392	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.493
7657	12591	\begin{align*} y^{\prime \prime }&=\frac {2 y}{x \left (x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.493
7658	15445	\begin{align*} x^{\prime }&=1+y \\ y^{\prime }&=1+x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.493
7659	16007	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.493
7660	16124	\begin{align*} y^{\prime \prime }+3 y^{\prime }+y&=\cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.493
7661	16179	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.493
7662	16609	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.493
7663	20168	\begin{align*} a y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.493
7664	21654	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&={\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.493
7665	23804	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.493
7666	24889	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.493
7667	25385	\begin{align*} y_{1}^{\prime }&=-2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+3 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.493
7668	6375	\begin{align*} x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.494
7669	9804	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.494
7670	12954	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	0.494
7671	16701	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.494
7672	17426	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.494
7673	17757	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.494
7674	18625	\begin{align*} y^{\prime } x&=-\frac {1}{\ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.494
7675	21632	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
7676	23320	\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.494
7677	23386	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.494
7678	23808	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.494
7679	24559	\begin{align*} y^{\prime \prime }+y&=12 \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.494
7680	1448	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.495
7681	3738	\begin{align*} y^{\prime \prime }+y&=3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.495
7682	6225	\begin{align*} 2 y+2 \left (-x +2\right ) y^{\prime }+\left (-x +2\right )^{2} x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.495
7683	7824	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.495
7684	12952	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (x +2 y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.495
7685	13779	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.495
7686	16003	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=2 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.495
7687	16068	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.495
7688	16161	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.495
7689	16936	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=5 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	0.495
7690	22190	\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+y x&=2+x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.495
7691	22256	\begin{align*} w^{\prime }+y&=\sin \left (t \right ) \\ y^{\prime }-z&={\mathrm e}^{t} \\ w+y+z^{\prime }&=1 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ w \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.495
7692	22294	\begin{align*} x^{\prime \prime }-3 x&=\sin \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	0.495
7693	22713	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.495
7694	23801	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.495
7695	23803	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.495
7696	23974	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.495
7697	25168	\begin{align*} y_{1}^{\prime }&=2 y_{2} \\ y_{2}^{\prime }&=-2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.495
7698	25265	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.495
7699	25272	\begin{align*} y^{\prime \prime }+y&=\sec \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.495
7700	2699	\begin{align*} x^{\prime }&=6 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.496