2.3.77 Problems 7601 to 7700

Table 2.703: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7601	22687	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.564
7602	22865	\begin{align*} \left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.564
7603	24676	\begin{align*} 4 y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.564
7604	2061	\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.565
7605	2582	\begin{align*} y^{\prime \prime }+y&=\sec \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.565
7606	2605	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.565
7607	3145	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.565
7608	5796	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.565
7609	9320	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.565
7610	17751	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.565
7611	17827	\begin{align*} x^{\prime }&=-3 x+6 y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.565
7612	19188	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.565
7613	21145	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{k t} \\ \end{align*}	✓	✓	✓	✓	0.565
7614	21912	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.565
7615	22734	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.565
7616	23075	\begin{align*} y^{\prime \prime }+2 y&=7 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.565
7617	2057	\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.566
7618	2391	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.566
7619	3178	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.566
7620	3719	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.566
7621	8285	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.566
7622	9472	\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.566
7623	10484	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.566
7624	13197	\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.566
7625	14103	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.566
7626	14608	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.566
7627	14611	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.566
7628	14625	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.566
7629	14739	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.566
7630	15771	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.566
7631	16109	\begin{align*} y^{\prime \prime }+4 y&=6+t^{2}+{\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.566
7632	16873	\begin{align*} y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.566
7633	19108	\begin{align*} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.566
7634	19500	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.566
7635	21539	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.566
7636	22292	\begin{align*} {s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \\ \end{align*}	✗	✗	✗	✗	0.566
7637	22726	\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.566
7638	23496	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.566
7639	23929	\begin{align*} 3 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.566
7640	26116	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3+x \,{\mathrm e}^{x}+x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.566
7641	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*}	✓	✓	✓	✓	0.567
7642	3861	\begin{align*} x_{1}^{\prime }&=4 x_{1} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ x_{3}^{\prime }&=x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.567
7643	3991	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.567
7644	5791	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.567
7645	7165	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.567
7646	7590	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.567
7647	7894	\begin{align*} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.567
7648	11727	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.567
7649	20703	\begin{align*} y^{\prime \prime }-4 y^{\prime }+y&=a \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.567
7650	20938	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=5 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.567
7651	21586	\begin{align*} y^{\prime \prime }-y&=x^{2}-x +1 \\ \end{align*}	✓	✓	✓	✓	0.567
7652	23039	\begin{align*} y^{\prime \prime }+5 y^{\prime }+8 y&=4 \sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.567
7653	24467	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.567
7654	24623	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.567
7655	25686	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}	✓	✓	✓	✓	0.567
7656	488	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.568
7657	505	\begin{align*} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.568
7658	1847	\begin{align*} \left (x +1\right ) y^{\prime \prime }+2 \left (x -1\right )^{2} y^{\prime }+3 y&=0 \\ y \left (1\right ) &= a_{0} \\ y^{\prime }\left (1\right ) &= a_{1} \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.568
7659	2045	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.568
7660	2233	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=40 x^{3} \\ y \left (-1\right ) &= -1 \\ y^{\prime }\left (-1\right ) &= -7 \\ y^{\prime \prime }\left (-1\right ) &= -1 \\ y^{\prime \prime \prime }\left (-1\right ) &= -31 \\ \end{align*}	✓	✓	✓	✓	0.568
7661	2427	\begin{align*} y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{t} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.568
7662	5390	\begin{align*} {y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.568
7663	9368	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.568
7664	9477	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.568
7665	13196	\(\left [\begin {array}{cccc} 1 & 0 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.568
7666	15048	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.568
7667	19562	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=-x^{4}+3 x \\ \end{align*}	✓	✓	✓	✓	0.568
7668	19772	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	0.568
7669	22192	\begin{align*} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.568
7670	23691	\begin{align*} \left (-x^{2}+4 x -3\right ) y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+6 y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.568
7671	23933	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ z^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.568
7672	473	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.569
7673	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*}	✓	✓	✓	✓	0.569
7674	1842	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.569
7675	3919	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=8 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.569
7676	3988	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.569
7677	4587	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.569
7678	9507	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.569
7679	9524	\begin{align*} y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✗	✗	0.569
7680	10502	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.569
7681	12890	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+x \,{\mathrm e}^{y}&=0 \\ \end{align*}	✗	✗	✗	✗	0.569
7682	14164	\begin{align*} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.569
7683	14610	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.569
7684	15433	\begin{align*} y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.569
7685	20931	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-5 x \\ \end{align*}	✓	✓	✓	✓	0.569
7686	21520	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.569
7687	21581	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.569
7688	21585	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.569
7689	22918	\begin{align*} x^{\prime }+x+2 y^{\prime }+3 y&=0 \\ x^{\prime }-2 x+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.569
7690	23526	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.569
7691	24018	\begin{align*} y^{\prime \prime \prime }+3 k y^{\prime \prime }+3 k^{2} y^{\prime }+k^{3} y&={\mathrm e}^{-x k} f^{\prime \prime \prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.569
7692	24433	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= {\mathrm e}^{3} \\ \end{align*}	✓	✓	✓	✓	0.569
7693	25524	\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.569
7694	25525	\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.569
7695	25604	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.569
7696	26413	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.569
7697	571	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=\delta \left (t \right )-\delta \left (-2+t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.570
7698	637	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.570
7699	6034	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.570
7700	10474	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.570