2.3.56 Problems 5501 to 5600

Table 2.685: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5501	25332	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.365
5502	26939	\begin{align*} y^{\prime \prime }+10 y^{\prime }+26 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
5503	965	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.366
5504	1012	\begin{align*} x_{1}^{\prime }&=7 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.366
5505	1760	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=7 x^{{3}/{2}} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.366
5506	2029	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
5507	2659	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.366
5508	2796	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=2 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.366
5509	8843	\begin{align*} x_{1}^{\prime }&=-x_{1}+3 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.366
5510	9667	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.366
5511	10153	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5512	10958	\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.366
5513	13672	\begin{align*} b y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5514	14048	\begin{align*} \left (x^{2}+1\right ) {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.366
5515	14195	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5516	14390	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.366
5517	14772	\begin{align*} x^{\prime }+y^{\prime }-x&=-2 t \\ x^{\prime }+y^{\prime }-3 x-y&=t^{2} \\ \end{align*}	✓	✓	✓	✗	0.366
5518	15714	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.366
5519	19482	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.366
5520	22153	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.366
5521	22794	\begin{align*} i^{\prime \prime \prime \prime }+9 i^{\prime \prime }&=20 \,{\mathrm e}^{-t} \\ i \left (0\right ) &= 0 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.366
5522	23996	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+2 y^{\prime }-y&=x^{4}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.366
5523	24544	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=6 x +6 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.366
5524	24632	\begin{align*} y^{\prime \prime }-9 y&=-72 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.366
5525	24698	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.366
5526	24869	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.366
5527	25365	\begin{align*} y_{1}^{\prime }&=3 y_{1}-y_{2} \\ y_{2}^{\prime }&=4 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.366
5528	25805	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5529	26957	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
5530	27585	\begin{align*} y y^{\prime }+x y y^{\prime \prime }-x {y^{\prime }}^{2}&=x^{3} \\ \end{align*}	✗	✓	✓	✗	0.366
5531	27594	\begin{align*} y^{\prime \prime }+2 y {y^{\prime }}^{2}&=\left (2 x +\frac {1}{x}\right ) y^{\prime } \\ \end{align*}	✗	✓	✓	✗	0.366
5532	27636	\begin{align*} y^{\prime \prime }-y&=2 \,{\mathrm e}^{x}-x^{2} \\ \end{align*}	✓	✓	✓	✓	0.366
5533	365	\begin{align*} y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.367
5534	657	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.367
5535	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*}	✓	✓	✓	✓	0.367
5536	6472	\begin{align*} 2 y y^{\prime \prime }&=4 y^{2} \left (x +2 y\right )+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.367
5537	6945	\begin{align*} x^{2}+\cos \left (x \right ) y+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.367
5538	8080	\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.367
5539	8112	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.367
5540	11066	\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.367
5541	12812	\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.367
5542	18860	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.367
5543	18920	\begin{align*} y_{1}^{\prime }&=y_{2}-y_{3} \\ y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t} \\ y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 2 \\ y_{3} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.367
5544	19049	\begin{align*} x_{1}^{\prime }&=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.367
5545	23391	\begin{align*} x^{5} y^{\left (5\right )}-2 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.367
5546	2614	\begin{align*} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(t=1\).	✓	✓	✓	✓	0.368
5547	4153	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8}&=\frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4} \\ \end{align*}	✓	✓	✓	✓	0.368
5548	6276	\begin{align*} 2 \left (1+3 x \right ) y+2 \left (2-3 x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
5549	7104	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.368
5550	7268	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5551	8038	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=\left (x^{2}-x +1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.368
5552	8796	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.368
5553	9230	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}	✓	✓	✓	✓	0.368
5554	9476	\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.368
5555	9728	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5556	10386	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.368
5557	10401	\begin{align*} y^{\prime \prime }+y&=x^{3}+x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.368
5558	10704	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
5559	11137	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5560	14406	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.368
5561	14957	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.368
5562	17601	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.368
5563	18111	\begin{align*} y^{\prime \prime \prime }+{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
5564	18211	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x^{2} {\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.368
5565	21212	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.368
5566	21917	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.368
5567	22129	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.368
5568	24655	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.368
5569	3854	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.369
5570	4158	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.369
5571	5494	\begin{align*} x^{2} {y^{\prime }}^{2}&=a^{2} \\ \end{align*}	✓	✓	✓	✓	0.369
5572	6696	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x \left (x^{2}+3\right ) \\ \end{align*}	✓	✓	✓	✓	0.369
5573	7457	\begin{align*} {\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5574	7586	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5575	9349	\begin{align*} y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
5576	9689	\begin{align*} x^{\prime }&=-x+3 y \\ y^{\prime }&=-3 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.369
5577	10234	\begin{align*} y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
5578	10647	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
5579	10706	\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5580	11272	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5581	13192	\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.369
5582	14185	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
5583	15011	\begin{align*} x^{\prime }&=-3 x-y \\ y^{\prime }&=x-5 y \\ \end{align*}	✓	✓	✓	✓	0.369
5584	15073	\begin{align*} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y}&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
5585	19201	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3}+3 x \\ \end{align*}	✓	✓	✓	✓	0.369
5586	20048	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y&=X \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
5587	21666	\begin{align*} y^{\prime \prime }&=y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.369
5588	22614	\begin{align*} 3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.369
5589	22777	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
5590	25136	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
5591	25138	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=10 t \,{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.369
5592	26534	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.369
5593	27714	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
5594	5778	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
5595	6331	\begin{align*} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.370
5596	7267	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
5597	8577	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.370
5598	18005	\begin{align*} x {y^{\prime }}^{2}&={\mathrm e}^{\frac {1}{y^{\prime }}} \\ \end{align*}	✓	✓	✓	✗	0.370
5599	19465	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
5600	23975	\begin{align*} y^{\prime \prime }-2 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.370