2.3.68 Problems 6701 to 6800

Table 2.709: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6701	19567	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.506
6702	26987	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.506
6703	27653	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=x \,{\mathrm e}^{-2 x} \cos \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.506
6704	27718	\begin{align*} -2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.506
6705	2231	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=9 x^{2} \\ y \left (1\right ) &= -7 \\ y^{\prime }\left (1\right ) &= -11 \\ y^{\prime \prime }\left (1\right ) &= -5 \\ y^{\prime \prime \prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.507
6706	3986	\begin{align*} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.507
6707	7102	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.507
6708	7202	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.507
6709	7280	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.507
6710	7358	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=6 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.507
6711	7814	\begin{align*} y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \\ \end{align*}	✓	✓	✓	✓	0.507
6712	8572	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.507
6713	20080	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.507
6714	20368	\begin{align*} y^{\prime \prime \prime \prime }-y&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.507
6715	21724	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }+4 y&=0 \\ \end{align*} With initial conditions \begin{align*} z \left (0\right ) &= -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.507
6716	22194	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.507
6717	22632	\begin{align*} i^{\prime \prime }-4 i^{\prime }+2 i&=0 \\ \end{align*}	✓	✓	✓	✓	0.507
6718	23075	\begin{align*} y^{\prime \prime }+2 y&=7 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.507
6719	23457	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.507
6720	23507	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{2 x} \left (x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.507
6721	25332	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.507
6722	25848	\begin{align*} y^{3} \sin \left (2 x \right )-3 y^{2} \cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.507
6723	27416	\begin{align*} {y^{\prime }}^{2}+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.507
6724	2232	\begin{align*} 4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y&=6 x \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 4 \\ y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\ \end{align*}	✓	✓	✓	✓	0.508
6725	7289	\begin{align*} 5 y^{\prime \prime }+12 y^{\prime }+20 y&=120 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.508
6726	9716	\begin{align*} {y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.508
6727	12842	\begin{align*} y^{\prime \prime }-2 y^{3} a^{2}+2 a b x y-b&=0 \\ \end{align*}	✗	✗	✗	✗	0.508
6728	15516	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.508
6729	16632	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.508
6730	17700	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.508
6731	20509	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y&=\ln \left (x \right )+x \\ \end{align*}	✓	✓	✓	✓	0.508
6732	21723	\begin{align*} x^{\prime }-6 x+3 y&=8 \,{\mathrm e}^{t} \\ y^{\prime }-2 x-y&=4 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.508
6733	21745	\begin{align*} x^{\prime }&=4 x-y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.508
6734	27360	\begin{align*} {y^{\prime }}^{2}+y x&=x y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	0.508
6735	925	\begin{align*} x^{\prime }&=y+z \\ y^{\prime }&=x+z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.509
6736	5787	\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.509
6737	5794	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.509
6738	7344	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=26 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.509
6739	8003	\begin{align*} y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.509
6740	8485	\begin{align*} y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.509
6741	9688	\begin{align*} x^{\prime }&=-6 x+5 y \\ y^{\prime }&=-5 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.509
6742	10508	\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.509
6743	10949	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.509
6744	12954	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	0.509
6745	16124	\begin{align*} y^{\prime \prime }+3 y^{\prime }+y&=\cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.509
6746	16127	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.509
6747	18694	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.509
6748	24660	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.509
6749	26555	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.509
6750	27155	\begin{align*} x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.509
6751	27361	\begin{align*} x y^{\prime } \left (x y^{\prime }+y\right )&=2 y^{2} \\ \end{align*}	✓	✓	✓	✓	0.509
6752	1865	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.510
6753	3176	\begin{align*} y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.510
6754	3711	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=4 x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	0.510
6755	7087	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.510
6756	8012	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.510
6757	9313	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.510
6758	10942	\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.510
6759	16895	\begin{align*} \left (x^{2}+4\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.510
6760	18770	\begin{align*} 25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.510
6761	19415	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.510
6762	19554	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.510
6763	19562	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=-x^{4}+3 x \\ \end{align*}	✓	✓	✓	✓	0.510
6764	20186	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=n^{2} y \\ \end{align*}	✓	✓	✓	✓	0.510
6765	21127	\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.510
6766	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*}	✓	✓	✓	✓	0.510
6767	27775	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.510
6768	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*}	✓	✓	✓	✗	0.511
6769	8851	\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.511
6770	9233	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.511
6771	9453	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.511
6772	10305	\begin{align*} {y^{\prime }}^{n}&=0 \\ \end{align*}	✓	✓	✓	✗	0.511
6773	11006	\begin{align*} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.511
6774	13014	\begin{align*} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \\ \end{align*}	✗	✗	✗	✗	0.511
6775	17822	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.511
6776	19425	\begin{align*} y^{\prime \prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.511
6777	19559	\begin{align*} 4 y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.511
6778	20347	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.511
6779	20467	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.511
6780	21938	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.511
6781	24790	\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*}	✓	✓	✓	✓	0.511
6782	24877	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.511
6783	26114	\begin{align*} 4 y+y^{\prime \prime }&=3 x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.511
6784	26126	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x+y+t \\ \end{align*}	✓	✓	✓	✓	0.511
6785	27696	\begin{align*} x^{3} y^{\prime \prime }-2 y x&=6 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.511
6786	976	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.512
6787	3237	\begin{align*} x^{\prime }+5 x&=3 t^{2} \\ y+y^{\prime }&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.512
6788	3427	\begin{align*} y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.512
6789	3710	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.512
6790	15195	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.512
6791	18758	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.512
6792	18761	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.512
6793	19508	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.512
6794	27698	\begin{align*} x^{2} y^{\prime \prime }-6 y&=5 x^{3}+8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.512
6795	526	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.513
6796	879	\begin{align*} y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.513
6797	896	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.513
6798	2585	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=t \,{\mathrm e}^{3 t}+1 \\ \end{align*}	✓	✓	✓	✓	0.513
6799	2702	\begin{align*} x^{\prime }&=x-3 y \\ y^{\prime }&=-2 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.513
6800	4120	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.513