2.3.66 Problems 6501 to 6600

Table 2.705: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6501	15193	\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.	✓	✓	✓	✓	0.493
6502	16014	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=-4 x+6 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.493
6503	19563	\begin{align*} y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.493
6504	23939	\begin{align*} y^{\prime }&=y+z+x \\ z^{\prime }&=1-y-z \\ \end{align*}	✓	✓	✓	✓	0.493
6505	24685	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=6 x^{2}-6 x -11 \\ \end{align*}	✓	✓	✓	✓	0.493
6506	628	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.494
6507	1389	\begin{align*} \left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
6508	1854	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
6509	3236	\begin{align*} x^{\prime }-x&=\cos \left (t \right ) \\ y+y^{\prime }&=4 t \\ \end{align*}	✓	✓	✓	✓	0.494
6510	3814	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.494
6511	3919	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=8 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.494
6512	4552	\begin{align*} x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.494
6513	9615	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.494
6514	10027	\begin{align*} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.494
6515	10463	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.494
6516	13932	\begin{align*} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.494
6517	16043	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-2 y \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.494
6518	16130	\begin{align*} y^{\prime \prime }+4 y&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.494
6519	19246	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.494
6520	19835	\begin{align*} y^{\prime \prime }-4 y^{\prime }+2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.494
6521	20933	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.494
6522	23597	\begin{align*} c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}} \\ c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}} \\ \end{align*}	✓	✓	✓	✓	0.494
6523	24033	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.494
6524	26121	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.494
6525	26745	\begin{align*} x^{\prime }+2 y^{\prime }&=17 x+8 y \\ 13 x^{\prime }&=53 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.494
6526	583	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=10 x-7 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	0.495
6527	1511	\begin{align*} y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.495
6528	7295	\begin{align*} 5 y^{\prime \prime }+6 y^{\prime }+2 y&=x^{2}+6 x \\ \end{align*}	✓	✓	✓	✓	0.495
6529	19187	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.495
6530	23846	\begin{align*} x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=1 \\ \end{align*}	✓	✓	✓	✗	0.495
6531	1860	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.496
6532	1932	\begin{align*} y^{\prime \prime }+\left (x^{2}+2 x +1\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.496
6533	2673	\begin{align*} y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.496
6534	7208	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.496
6535	7283	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.496
6536	7905	\begin{align*} y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.496
6537	7999	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.496
6538	9455	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.496
6539	10474	\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.496
6540	10484	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.496
6541	10502	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.496
6542	12337	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.496
6543	15218	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.496
6544	16068	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.496
6545	19026	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.496
6546	20206	\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.496
6547	20847	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=10 \\ \end{align*}	✓	✓	✓	✓	0.496
6548	20940	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=3 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.496
6549	23505	\begin{align*} y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\ \end{align*}	✓	✓	✓	✓	0.496
6550	23574	\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}	✓	✓	✓	✓	0.496
6551	23577	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.496
6552	24586	\begin{align*} y^{\prime \prime }+y&=1+4 x \\ \end{align*}	✓	✓	✓	✓	0.496
6553	26951	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= 12 \\ y^{\prime }\left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.496
6554	1020	\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{3} \\ x_{2}^{\prime }&=x_{2}-4 x_{3} \\ x_{3}^{\prime }&=x_{2}-3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.497
6555	1739	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.497
6556	1818	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=6 \,{\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.497
6557	2551	\begin{align*} y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.497
6558	3920	\begin{align*} x_{1}^{\prime }&=-6 x_{2} \\ x_{2}^{\prime }&=x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.497
6559	4513	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=60 \cos \left (3 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.497
6560	8564	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.497
6561	8795	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=1+3 x \\ \end{align*}	✓	✓	✓	✓	0.497
6562	10388	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.497
6563	10478	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.497
6564	12552	\begin{align*} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.497
6565	14993	\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.497
6566	15187	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.497
6567	16508	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 14 \\ \end{align*}	✓	✓	✓	✓	0.497
6568	16510	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.497
6569	18886	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.497
6570	26954	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=0 \\ y \left (-4\right ) &= 7 \\ y^{\prime }\left (-4\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.497
6571	27160	\begin{align*} x_{1}^{\prime }&=x_{1}+5 x_{2} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=4 x_{1}+8 x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.497
6572	1858	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.498
6573	7288	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.498
6574	7790	\begin{align*} y^{\prime \prime }-5 y&=2 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.498
6575	7997	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.498
6576	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.	✓	✓	✓	✓	0.498
6577	11734	\begin{align*} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.498
6578	12952	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (x +2 y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.498
6579	13062	\begin{align*} x^{\prime }&=a x-y \\ y^{\prime }&=x+a y \\ \end{align*}	✓	✓	✓	✓	0.498
6580	16258	\begin{align*} y^{\prime }-x y^{2}&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✗	0.498
6581	18002	\begin{align*} x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\ \end{align*}	✓	✓	✓	✓	0.498
6582	20882	\begin{align*} y^{\prime }&=2 y x -x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.498
6583	24657	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.498
6584	26961	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \cos \left (x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.498
6585	1861	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.499
6586	11291	\begin{align*} y^{\prime \prime }&=\frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.499
6587	19836	\begin{align*} y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.499
6588	23556	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.499
6589	23758	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.499
6590	25167	\begin{align*} y_{1}^{\prime }-3 y_{1}&=-4 y_{2} \\ y_{2}^{\prime }+y_{2}&=y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.499
6591	25625	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.499
6592	27094	\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 1 & 0 & 2 \\ 0 & 0 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.499
6593	613	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.500
6594	630	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.500
6595	1388	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y x&=0 \\ \end{align*} Series expansion around \(x=4\).	✓	✓	✓	✓	0.500
6596	1883	\begin{align*} \left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.500
6597	2618	\begin{align*} y^{\prime \prime }-2 t y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.500
6598	3923	\begin{align*} x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.500
6599	6777	\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.500
6600	7787	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=50 t^{3}-36 t^{2}-63 t +18 \\ \end{align*}	✓	✓	✓	✓	0.500