2.3.54 Problems 5301 to 5400

Table 2.681: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5301	24501	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.417
5302	25159	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.417
5303	26931	\begin{align*} y^{\prime \prime }-16 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.417
5304	1333	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.418
5305	2681	\begin{align*} y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.418
5306	2777	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.418
5307	3884	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.418
5308	3926	\begin{align*} x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.418
5309	6738	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.418
5310	7198	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.418
5311	8099	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.418
5312	8173	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
5313	9315	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
5314	10297	\begin{align*} \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
5315	16640	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=100 \\ \end{align*}	✓	✓	✓	✓	0.418
5316	16706	\begin{align*} y^{\prime \prime \prime \prime }-81 y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.418
5317	17863	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.418
5318	21641	\begin{align*} y^{\prime \prime }&=x y^{2}-y^{\prime } \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.418
5319	21704	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (\pi \right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.418
5320	22677	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
5321	23317	\begin{align*} 3 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
5322	23561	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.418
5323	24778	\begin{align*} {y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
5324	26701	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=\cos \left (2 x \right ) \\ y \left (0\right ) &= {\frac {1}{25}} \\ y \left (\pi \right ) &= {\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= {\frac {2}{15}} \\ y^{\prime }\left (\pi \right ) &= {\frac {2}{25}} \\ \end{align*}	✓	✓	✓	✓	0.418
5325	452	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.419
5326	456	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.419
5327	2379	\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.419
5328	3324	\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.419
5329	4091	\begin{align*} y^{\prime }&=1-x^{5}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.419
5330	14991	\(\left [\begin {array}{cc} 2 & 2 \\ 0 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.419
5331	16061	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-2 x+y \\ \end{align*}	✓	✓	✓	✓	0.419
5332	17828	\begin{align*} x^{\prime }&=8 x-y \\ y^{\prime }&=x+6 y \\ \end{align*}	✓	✓	✓	✓	0.419
5333	20421	\begin{align*} y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	0.419
5334	25095	\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.419
5335	27684	\begin{align*} y^{\prime \prime }+y&=4 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.419
5336	865	\begin{align*} 2 x^{\prime \prime }+12 x^{\prime }+50 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.420
5337	1443	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.420
5338	2229	\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y&=9 x^{4} \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.420
5339	2239	\begin{align*} y_{1}^{\prime }&=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\ y_{2}^{\prime }&=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \\ \end{align*}	✓	✓	✓	✓	0.420
5340	7806	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.420
5341	7839	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.420
5342	10646	\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*}	✓	✓	✓	✗	0.420
5343	16003	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=2 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.420
5344	20059	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.420
5345	23580	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.420
5346	25180	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.420
5347	40	\begin{align*} y^{\prime }&=x +\frac {y^{2}}{2} \\ y \left (-2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.421
5348	568	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=2 \delta \left (t -\pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.421
5349	580	\begin{align*} x^{\prime }&=\frac {y}{2} \\ y^{\prime }&=-8 x \\ \end{align*}	✓	✓	✓	✓	0.421
5350	1387	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.421
5351	2294	\begin{align*} y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.421
5352	3113	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.421
5353	3274	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \cos \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✗	✗	✗	0.421
5354	3615	\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.421
5355	9808	\begin{align*} 6 {y^{\prime }}^{2} x -\left (3 x +2 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.421
5356	14087	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.421
5357	16005	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.421
5358	18177	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.421
5359	19578	\begin{align*} y^{\prime }&=2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.421
5360	23570	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.421
5361	23813	\begin{align*} x^{\prime }&=4 x+6 y \\ y^{\prime }&=-7 x-9 y \\ \end{align*}	✓	✓	✓	✓	0.421
5362	24433	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= {\mathrm e}^{3} \\ \end{align*}	✓	✓	✓	✓	0.421
5363	24474	\begin{align*} y^{\prime \prime }-4 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.421
5364	24805	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.421
5365	972	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.422
5366	3693	\begin{align*} y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.422
5367	5381	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
5368	7278	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.422
5369	7842	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.422
5370	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*}	✓	✓	✓	✗	0.422
5371	12777	\begin{align*} y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.422
5372	15496	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
5373	16004	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.422
5374	19243	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.422
5375	19880	\begin{align*} z^{\prime }+7 y-3 z&=0 \\ 7 y^{\prime }+63 y-36 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
5376	22072	\begin{align*} y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.422
5377	23360	\begin{align*} 6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
5378	23827	\begin{align*} x^{\prime }&=-3 x+2 y \\ y^{\prime }&=-2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.422
5379	25106	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
5380	25241	\begin{align*} t y^{\prime \prime }-4 y^{\prime }+y t&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.422
5381	27062	\begin{align*} y^{\prime }-y x&=1-x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.422
5382	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*}	✓	✓	✓	✓	0.423
5383	6617	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.423
5384	12511	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (a -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.423
5385	14189	\begin{align*} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.423
5386	17585	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.423
5387	19472	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.423
5388	19583	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.423
5389	25627	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.423
5390	27153	\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.423
5391	27590	\begin{align*} 2 x y^{2} \left (x y^{\prime \prime }+y^{\prime }\right )+1&=0 \\ \end{align*}	✗	✓	✓	✗	0.423
5392	27676	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.423
5393	27774	\begin{align*} 9 x^{2} y^{\prime \prime }-\left (x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.423
5394	291	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.424
5395	1084	\begin{align*} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.424
5396	1369	\begin{align*} \left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.424
5397	1442	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.424
5398	3812	\begin{align*} x_{1}^{\prime }&=2 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-4 x_{1}-6 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.424
5399	10158	\begin{align*} y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.424
5400	12363	\begin{align*} x y^{\prime \prime }-y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.424