2.3.52 Problems 5101 to 5200

Table 2.677: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5101	8552	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5102	10719	\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.404
5103	12368	\begin{align*} a \,x^{2} y+2 y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.404
5104	15991	\begin{align*} x^{\prime }&=3 x+4 y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.404
5105	16937	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.404
5106	20885	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5107	23016	\begin{align*} z^{\prime \prime }-3 z^{\prime }+z&=0 \\ z \left (0\right ) &= 1 \\ z^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.404
5108	23306	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.404
5109	23647	\begin{align*} y^{\prime }-3 y&=2 \,{\mathrm e}^{t} \\ y \left (1\right ) &= {\mathrm e}^{3}-{\mathrm e} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.404
5110	24078	\begin{align*} 4 y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5111	24117	\begin{align*} y^{\prime }-y&=x^{2}+1 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5112	25063	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.404
5113	25635	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.404
5114	26242	\begin{align*} {\mathrm e}^{y^{\prime }}&=1 \\ \end{align*}	✓	✓	✓	✓	0.404
5115	2412	\begin{align*} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.405
5116	6942	\begin{align*} y-3 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5117	16000	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.405
5118	18114	\begin{align*} 3 y^{\prime } y^{\prime \prime }&=2 y \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.405
5119	20342	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.405
5120	20508	\begin{align*} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.405
5121	21291	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.405
5122	22681	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5123	23320	\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5124	25077	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.405
5125	26116	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3+x \,{\mathrm e}^{x}+x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.405
5126	7942	\begin{align*} {y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.406
5127	8612	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.406
5128	10614	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.406
5129	17361	\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.406
5130	19844	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.406
5131	21487	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.406
5132	576	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.407
5133	2259	\begin{align*} y_{1}^{\prime }&=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+11 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.407
5134	7586	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.407
5135	18101	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.407
5136	21909	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.407
5137	25952	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.407
5138	394	\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.408
5139	975	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.408
5140	1365	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5141	1424	\begin{align*} x_{1}^{\prime }&=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.408
5142	1890	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5143	2238	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2} \\ y_{2}^{\prime }&=2 y_{1}+y_{2} \\ \end{align*}	✓	✓	✓	✓	0.408
5144	2679	\begin{align*} y^{\prime \prime }+y&=t \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.408
5145	4118	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5146	6669	\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5147	7089	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.408
5148	7496	\begin{align*} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5149	8174	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.408
5150	9068	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.408
5151	10860	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.408
5152	13198	\(\left [\begin {array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.408
5153	16013	\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*}	✓	✓	✓	✓	0.408
5154	19462	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5155	19470	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5156	19586	\begin{align*} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5157	20662	\begin{align*} \left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.408
5158	23689	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5159	24711	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.408
5160	24777	\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5161	25323	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.408
5162	26958	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\alpha ^{2} y&=0 \\ y \left (0\right ) &= c \\ y^{\prime }\left (0\right ) &= d \\ \end{align*}	✓	✓	✓	✓	0.408
5163	621	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.409
5164	1444	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.409
5165	2258	\begin{align*} y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.409
5166	3855	\begin{align*} x_{1}^{\prime }&=-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.409
5167	8902	\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.409
5168	14112	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=3 x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.409
5169	16314	\begin{align*} {\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.409
5170	16471	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -9 \\ \end{align*}	✓	✓	✓	✓	0.409
5171	16484	\begin{align*} y^{\prime \prime }-10 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -24 \\ \end{align*}	✓	✓	✓	✓	0.409
5172	20943	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.409
5173	25540	\begin{align*} y^{\prime \prime }&=2 a y^{\prime }-\left (a^{2}-\omega ^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.409
5174	25747	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.409
5175	26741	\begin{align*} x^{\prime }&=-4 x-4 y \\ x^{\prime }+4 y^{\prime }&=-4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.409
5176	219	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.410
5177	427	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.410
5178	971	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.410
5179	1682	\begin{align*} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
5180	3337	\begin{align*} y^{\prime }&=3 x +\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.410
5181	9618	\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.410
5182	16427	\begin{align*} y^{\prime \prime }&=-2 {y^{\prime }}^{2} x \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.410
5183	19465	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
5184	25103	\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
5185	26347	\begin{align*} {y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.410
5186	27770	\begin{align*} x y^{\prime \prime }+y \ln \left (1-x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.410
5187	406	\begin{align*} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
5188	1089	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
5189	1526	\begin{align*} y^{\prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.411
5190	3894	\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.411
5191	6944	\begin{align*} 2 y x +x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
5192	7852	\begin{align*} y^{\prime \prime }-y&=4-x \\ \end{align*}	✓	✓	✓	✓	0.411
5193	7887	\begin{align*} x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
5194	8074	\begin{align*} y^{\prime \prime }-x y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
5195	9221	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
5196	9239	\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
5197	10270	\begin{align*} c y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
5198	10351	\begin{align*} x y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.411
5199	11312	\begin{align*} y^{\prime }+f^{\prime }\left (x \right ) y-f \left (x \right ) f^{\prime }\left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
5200	12360	\begin{align*} x y^{\prime \prime }+y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411