2.3.77 Problems 7601 to 7700

Table 2.685: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7601	20724	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.382
7602	21131	\begin{align*} x^{\prime \prime }-4 x&=4 t^{2} \\ \end{align*}	✓	✓	✓	✓	0.382
7603	21219	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.382
7604	1449	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2} \\ x_{2}^{\prime }&=-\frac {5 x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.383
7605	1875	\begin{align*} \left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y&=0 \\ y \left (3\right ) &= 4 \\ y^{\prime }\left (3\right ) &= -6 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.383
7606	3199	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	0.383
7607	7208	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.383
7608	7795	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.383
7609	8848	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=3 x_{1}-4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.383
7610	9469	\begin{align*} x^{\prime }&=7 x+6 y \\ y^{\prime }&=2 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.383
7611	9700	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.383
7612	9857	\begin{align*} y^{\prime \prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.383
7613	14860	\begin{align*} x^{\prime }&=x+7 y \\ y^{\prime }&=3 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.383
7614	14958	\begin{align*} x^{\prime \prime }-x&=\frac {1}{t} \\ \end{align*}	✓	✓	✓	✓	0.383
7615	22205	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.383
7616	22281	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=9 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.383
7617	23494	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.383
7618	615	\begin{align*} x_{1}^{\prime }&=4 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-7 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 8 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.384
7619	897	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.384
7620	1291	\begin{align*} y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \alpha \\ \end{align*}	✓	✓	✓	✓	0.384
7621	1865	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.384
7622	2593	\begin{align*} y^{\prime \prime }+3 y&=t^{3}-1 \\ \end{align*}	✓	✓	✓	✓	0.384
7623	3209	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.384
7624	5663	\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.384
7625	6091	\begin{align*} -12 y-8 y^{\prime } x +\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.384
7626	7072	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.384
7627	8798	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.384
7628	14296	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.384
7629	14939	\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.384
7630	16019	\begin{align*} x^{\prime }&=-\frac {9 x}{10}-2 y \\ y^{\prime }&=x+\frac {11 y}{10} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.384
7631	16867	\begin{align*} y^{\prime }+y \ln \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.384
7632	17748	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=-t \\ \end{align*}	✓	✓	✓	✓	0.384
7633	18193	\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.384
7634	24564	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-3 x} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.384
7635	25665	\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align*}	✓	✓	✓	✓	0.384
7636	355	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.385
7637	390	\begin{align*} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.385
7638	968	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.385
7639	1387	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385
7640	1860	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385
7641	1906	\begin{align*} \left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -7 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385
7642	2238	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2} \\ y_{2}^{\prime }&=2 y_{1}+y_{2} \\ \end{align*}	✓	✓	✓	✓	0.385
7643	4003	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=2 \cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.385
7644	6686	\begin{align*} 10 y^{\prime }+8 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.385
7645	8098	\begin{align*} \left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385
7646	8259	\begin{align*} y^{\prime }&=2 y-4 \\ \end{align*}	✓	✓	✓	✓	0.385
7647	9248	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}	✓	✓	✓	✓	0.385
7648	9515	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385
7649	9671	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.385
7650	10262	\begin{align*} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.385
7651	12415	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
7652	13185	\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.385
7653	13186	\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.385
7654	14156	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
7655	14167	\begin{align*} y^{\prime }+\left (2+x \right ) y^{\prime \prime }+\left (2+x \right )^{2} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✗	0.385
7656	16631	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.385
7657	16669	\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.385
7658	17354	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.385
7659	18940	\begin{align*} y^{\prime \prime }-y&=-20 \delta \left (t -3\right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.385
7660	21135	\begin{align*} x^{\prime \prime }-x&=3 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.385
7661	22875	\begin{align*} y^{\prime \prime } x +y^{\prime }-i x y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.385
7662	23495	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (x^{2}-1\right ) \\ \end{align*}	✓	✓	✓	✓	0.385
7663	1843	\begin{align*} \left (3 x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.386
7664	6236	\begin{align*} a^{2} y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.386
7665	6551	\begin{align*} x y^{2} y^{\prime \prime }&=\left (a -y^{2}\right ) y^{\prime }+x y {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.386
7666	7216	\begin{align*} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.386
7667	7298	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.386
7668	7797	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.386
7669	10001	\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	0.386
7670	10029	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.386
7671	10162	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.386
7672	10403	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.386
7673	10449	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.386
7674	11852	\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✗	0.386
7675	12584	\begin{align*} \left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.386
7676	13027	\begin{align*} \left (-y+y^{\prime } x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.386
7677	13158	\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.386
7678	14855	\begin{align*} x^{\prime }&=3 x+4 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.386
7679	16606	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✓	0.386
7680	16656	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{2 x} \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.386
7681	17594	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=-\sec \left (t \right ) \tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.386
7682	18793	\begin{align*} y^{\prime \prime }+6 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.386
7683	19466	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.386
7684	21134	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.386
7685	21586	\begin{align*} y^{\prime \prime }-y&=x^{2}-x +1 \\ \end{align*}	✓	✓	✓	✓	0.386
7686	23078	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=2 x^{3}+7 x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.386
7687	23686	\begin{align*} \left (x +3\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.386
7688	6958	\begin{align*} y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
7689	7287	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.387
7690	7757	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.387
7691	9674	\begin{align*} x^{\prime }&=10 x-5 y \\ y^{\prime }&=8 x-12 y \\ \end{align*}	✓	✓	✓	✓	0.387
7692	10549	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
7693	13159	\(\left [\begin {array}{ccc} 5 & -6 & 3 \\ 6 & -7 & 3 \\ 6 & -6 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.387
7694	16018	\begin{align*} x^{\prime }&=x+4 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.387
7695	20584	\begin{align*} 2 x^{2} y y^{\prime \prime }+y^{2}&=x^{2} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.387
7696	20739	\begin{align*} {y^{\prime }}^{3}-4 x y^{\prime } y+8 y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.387
7697	23043	\begin{align*} z^{\prime \prime }-4 z&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.387
7698	23366	\begin{align*} y^{\prime \prime }-2 r y^{\prime }+\left (r^{2}-\frac {\alpha ^{2}}{4}\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.387
7699	879	\begin{align*} y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.388
7700	1515	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.388