2.3.59 Problems 5801 to 5900

Table 2.691: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5801	24080	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.450
5802	25324	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.450
5803	26094	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.450
5804	26934	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=-5 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.450
5805	26967	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.450
5806	27366	\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }&=8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.450
5807	27601	\begin{align*} x^{2} y y^{\prime \prime }+1&=x \left (1-y\right ) y^{\prime } \\ \end{align*}	✗	✓	✓	✗	0.450
5808	365	\begin{align*} y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.451
5809	624	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.451
5810	655	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {x +2}} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.451
5811	856	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.451
5812	3284	\begin{align*} 4 y^{2}&={y^{\prime }}^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.451
5813	7071	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.451
5814	7103	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.451
5815	7763	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.451
5816	8023	\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.451
5817	10671	\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \\ \end{align*}	✓	✓	✓	✗	0.451
5818	11716	\begin{align*} \left (5+3 x \right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.451
5819	17411	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.451
5820	18317	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	0.451
5821	20620	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.451
5822	22232	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.451
5823	24031	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.451
5824	25109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.451
5825	8483	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.452
5826	14574	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.452
5827	16066	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.452
5828	1924	\begin{align*} y^{\prime \prime }+5 x y^{\prime }-\left (-x^{2}+3\right ) y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.453
5829	2268	\begin{align*} y_{1}^{\prime }&=-7 y_{1}+24 y_{2} \\ y_{2}^{\prime }&=-6 y_{1}+17 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 3 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.453
5830	3406	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.453
5831	4587	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.453
5832	6703	\begin{align*} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.453
5833	7299	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.453
5834	10076	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.453
5835	14376	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.453
5836	15199	\begin{align*} y^{\prime \prime }-20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -14 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.453
5837	16167	\begin{align*} y^{\prime }&=x \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.453
5838	16988	\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\ \end{align*}	✓	✓	✓	✓	0.453
5839	21110	\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.453
5840	23101	\begin{align*} x y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.453
5841	520	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5842	1313	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.454
5843	1905	\begin{align*} y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.454
5844	1926	\begin{align*} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.454
5845	3115	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.454
5846	6702	\begin{align*} 2 y-2 x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5847	9062	\begin{align*} y^{\prime }&={\mathrm e}^{3 x}-x \\ \end{align*}	✓	✓	✓	✓	0.454
5848	9225	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5849	10412	\begin{align*} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.454
5850	10477	\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.454
5851	13066	\begin{align*} x^{\prime }+3 x+4 y&=0 \\ y^{\prime }+2 x+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5852	13158	\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.454
5853	14798	\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.454
5854	16641	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.454
5855	16642	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=10 x^{2}+4 x +8 \\ \end{align*}	✓	✓	✓	✓	0.454
5856	18466	\begin{align*} x^{\prime \prime }-x^{\prime }&=1 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.454
5857	18774	\begin{align*} y^{\prime \prime }-9 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5858	21109	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5859	21210	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.454
5860	21637	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.454
5861	23555	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+6 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.454
5862	26717	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.454
5863	579	\begin{align*} x^{\prime }&=10 y \\ y^{\prime }&=-10 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.455
5864	868	\begin{align*} x^{\prime \prime }+10 x^{\prime }+125 x&=0 \\ x \left (0\right ) &= 6 \\ x^{\prime }\left (0\right ) &= 50 \\ \end{align*}	✓	✓	✓	✓	0.455
5865	2242	\begin{align*} y_{1}^{\prime }&=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.455
5866	14814	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.455
5867	14816	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.455
5868	15201	\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.455
5869	19695	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.455
5870	19892	\begin{align*} {y^{\prime }}^{2}+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.455
5871	20179	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.455
5872	21876	\begin{align*} 9 y^{\prime \prime }-30 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.455
5873	540	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=6 x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	0.456
5874	627	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.456
5875	3996	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.456
5876	12918	\begin{align*} y y^{\prime \prime }-a \,x^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.456
5877	15981	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=2 x-5 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.456
5878	18697	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.456
5879	19033	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 4 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.456
5880	24641	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.456
5881	26374	\begin{align*} {y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	0.456
5882	578	\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*}	✓	✓	✓	✓	0.457
5883	634	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.457
5884	1406	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.457
5885	1878	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.457
5886	3120	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.457
5887	7594	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*}	✓	✓	✓	✓	0.457
5888	7730	\begin{align*} y^{\prime }-2 y \tan \left (x \right )&=y^{2} \tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.457
5889	7899	\begin{align*} -y-3 \left (x^{2}+y^{2}\right ) x^{2}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.457
5890	9178	\begin{align*} x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.457
5891	9316	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.457
5892	13159	\(\left [\begin {array}{ccc} 5 & -6 & 3 \\ 6 & -7 & 3 \\ 6 & -6 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.457
5893	13194	\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.457
5894	14795	\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.457
5895	15200	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.457
5896	19163	\begin{align*} {y^{\prime \prime }}^{2}-2 x y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.457
5897	20519	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y&=x^{2}+3 x -4 \\ \end{align*}	✓	✓	✓	✓	0.457
5898	23579	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.457
5899	24779	\begin{align*} {y^{\prime }}^{2}-x^{2} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.457
5900	27572	\begin{align*} x^{2} y y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{2} \\ \end{align*}	✗	✓	✓	✗	0.457