2.3.58 Problems 5701 to 5800

Table 2.647: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5701	1274	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.298
5702	1362	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.298
5703	5482	\begin{align*} \left (a -x \right ) {y^{\prime }}^{2}+y^{\prime } y-b&=0 \\ \end{align*}	✓	✓	✓	✗	0.298
5704	6305	\begin{align*} y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y+2 y^{3} \\ \end{align*}	✗	✗	✗	✗	0.298
5705	6480	\begin{align*} 2 y y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.298
5706	18688	\begin{align*} x^{\prime }&=-x-\frac {y}{2} \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.298
5707	23993	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.298
5708	24630	\begin{align*} y^{\prime \prime }-4 y&=16 \,{\mathrm e}^{-2 x} x +8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.298
5709	25330	\begin{align*} \left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.298
5710	1528	\begin{align*} y^{\prime }&=x \sin \left (x^{2}\right ) \\ y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.299
5711	1867	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.299
5712	1887	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.299
5713	2378	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
5714	3421	\begin{align*} y^{\prime }&=\frac {t}{t^{2}+4} \\ \end{align*}	✓	✓	✓	✓	0.299
5715	4299	\begin{align*} \frac {x}{y^{2}+x^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{y^{2}+x^{2}}-\frac {1}{x}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.299
5716	5717	\begin{align*} y^{\prime \prime }+y&=a x \\ \end{align*}	✓	✓	✓	✓	0.299
5717	6569	\begin{align*} \sqrt {y}\, y^{\prime \prime }&=2 b x +2 a \\ \end{align*}	✗	✓	✗	✗	0.299
5718	6946	\begin{align*} x^{2}+y^{2}+x +x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
5719	7104	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.299
5720	8578	\begin{align*} \left (x -2\right ) y^{\prime }&=y x \\ y \left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.299
5721	9225	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
5722	10678	\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
5723	11379	\begin{align*} y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b&=0 \\ \end{align*}	✓	✓	✓	✓	0.299
5724	12545	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.299
5725	13166	\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.299
5726	14360	\begin{align*} x^{\prime }&=2 x+\operatorname {Heaviside}\left (-1+t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.299
5727	16027	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=x-4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.299
5728	16882	\begin{align*} \left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.299
5729	16991	\begin{align*} y^{\prime }&=\cot \left (x \right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.299
5730	17661	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=-8 \\ \end{align*}	✓	✓	✓	✓	0.299
5731	18687	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}	✓	✓	✓	✓	0.299
5732	23004	\begin{align*} 8 y^{\prime \prime }-10 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.299
5733	23934	\begin{align*} y^{\prime }&=z \\ z^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.299
5734	24671	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.299
5735	25116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.299
5736	25248	\begin{align*} t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.299
5737	25553	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	0.299
5738	25589	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.299
5739	427	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.300
5740	515	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.300
5741	812	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.300
5742	1088	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.300
5743	2623	\begin{align*} y^{\prime \prime }+y^{\prime }+t y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.300
5744	2779	\begin{align*} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.300
5745	4510	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 \ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	0.300
5746	9264	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.300
5747	9687	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=9 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.300
5748	10601	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.300
5749	10633	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.300
5750	10694	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.300
5751	11020	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.300
5752	14999	\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.300
5753	16026	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.300
5754	16028	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.300
5755	16833	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.300
5756	17685	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.300
5757	18686	\begin{align*} x^{\prime }&=-\frac {3 x}{2}+y \\ y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\ \end{align*}	✓	✓	✓	✓	0.300
5758	18817	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.300
5759	20922	\begin{align*} x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\ y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.300
5760	22749	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.300
5761	23360	\begin{align*} 6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.300
5762	23814	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.300
5763	24562	\begin{align*} y^{\prime \prime }-4 y&=2-8 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.300
5764	24708	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.300
5765	24756	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.300
5766	25759	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.300
5767	621	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.301
5768	1076	\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.301
5769	1078	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.301
5770	1276	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
5771	3308	\begin{align*} x&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.301
5772	6178	\begin{align*} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
5773	6243	\begin{align*} -\left (x +1\right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.301
5774	7075	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.301
5775	8636	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\ y \left (\frac {3}{2}\right ) &= 4 \\ y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.301
5776	10197	\begin{align*} x^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.301
5777	16649	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.301
5778	20746	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.301
5779	21874	\begin{align*} y^{\prime \prime }-12 y^{\prime }+35 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
5780	22291	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.301
5781	23787	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.301
5782	24430	\begin{align*} y^{\prime \prime }-4 a y^{\prime }+3 a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
5783	24849	\begin{align*} 5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.301
5784	24949	\begin{align*} y y^{\prime }&=1-y \\ \end{align*}	✓	✓	✓	✓	0.301
5785	25318	\begin{align*} y^{\prime \prime }-y&=\delta \left (-1+t \right )-\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.301
5786	25563	\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.301
5787	25566	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=5 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.301
5788	467	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.302
5789	854	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.302
5790	2548	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.302
5791	6195	\begin{align*} \left (c x +b \right ) y+a \,x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.302
5792	6689	\begin{align*} y^{\prime }+\left (2+x \right ) y^{\prime \prime }+\left (2+x \right )^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.302
5793	6863	\begin{align*} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.302
5794	6865	\begin{align*} x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.302
5795	7279	\begin{align*} y^{\prime \prime }+y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.302
5796	8483	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.302
5797	9313	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 y^{\prime \prime } x -8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.302
5798	10295	\begin{align*} y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	0.302
5799	10482	\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.302
5800	10704	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.302