2.3.53 Problems 5201 to 5300

Table 2.679: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5201	12550	\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
5202	16494	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.411
5203	17778	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
5204	20489	\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}	✓	✓	✓	✓	0.411
5205	23258	\begin{align*} y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.411
5206	23712	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
5207	23839	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ \end{align*}	✓	✓	✓	✓	0.411
5208	25073	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
5209	25102	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
5210	26746	\begin{align*} x^{\prime }&=y \\ x^{\prime }-y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (\pi \right ) &= -1 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.411
5211	432	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
5212	433	\begin{align*} \left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
5213	1525	\begin{align*} y^{\prime }&=-x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.412
5214	3506	\begin{align*} y^{\prime \prime }-2 z y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.412
5215	10289	\begin{align*} x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
5216	10553	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
5217	14353	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.412
5218	15998	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
5219	16034	\begin{align*} x^{\prime }&=-3 x-y \\ y^{\prime }&=4 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.412
5220	16821	\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
5221	18133	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
5222	19438	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.412
5223	19642	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.412
5224	23605	\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*}	✓	✓	✓	✓	0.412
5225	23693	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
5226	23821	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.412
5227	25628	\begin{align*} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.412
5228	26927	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.412
5229	381	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✗	0.413
5230	2257	\begin{align*} y_{1}^{\prime }&=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }&=-3 y_{1}-8 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.413
5231	7684	\begin{align*} x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.413
5232	12421	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{k}-b \left (b -1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.413
5233	23042	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.413
5234	23697	\begin{align*} \left (x^{2}+4 x +3\right ) y^{\prime \prime }+2 \left (x +2\right ) y^{\prime }-2 y&=0 \\ y \left (-2\right ) &= 0 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.413
5235	23715	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.413
5236	23833	\begin{align*} y^{\prime }&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.413
5237	24437	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.413
5238	26484	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.413
5239	26932	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=15 \\ \end{align*}	✓	✓	✓	✓	0.413
5240	27193	\begin{align*} x_{1}^{\prime }&=2 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-10 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.413
5241	871	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
5242	1489	\begin{align*} y^{\prime \prime \prime \prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.414
5243	3856	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.414
5244	6655	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.414
5245	7592	\begin{align*} 4 w^{\prime \prime }+20 w^{\prime }+25 w&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5246	7901	\begin{align*} 3 x^{2}+y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5247	8627	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \\ y \left (0\right ) &= {\frac {16}{5}} \\ y^{\prime }\left (0\right ) &= {\frac {31}{5}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.414
5248	9033	\begin{align*} {\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5249	13156	\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.414
5250	16995	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.414
5251	20215	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5252	20353	\begin{align*} y^{\prime \prime }-4 y&=2 \sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.414
5253	23293	\begin{align*} 3 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.414
5254	23571	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.414
5255	23774	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.414
5256	23829	\begin{align*} y^{\prime }&=\cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.414
5257	24857	\begin{align*} {y^{\prime }}^{2} x -\left (x^{2}+1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5258	25100	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5259	25633	\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.414
5260	26946	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.414
5261	155	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.415
5262	581	\begin{align*} x^{\prime }&=8 y \\ y^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.415
5263	964	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.415
5264	1287	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.415
5265	1376	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.415
5266	2610	\begin{align*} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.415
5267	3172	\begin{align*} 4 y+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.415
5268	3895	\begin{align*} x_{1}^{\prime }&=-8 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-5 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.415
5269	7347	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.415
5270	7449	\begin{align*} y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
5271	7755	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=8 \\ \end{align*}	✓	✓	✓	✓	0.415
5272	16007	\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*}	✓	✓	✓	✓	0.415
5273	16522	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.415
5274	20154	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y&=2 x \\ \end{align*}	✓	✓	✓	✗	0.415
5275	20205	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&=0 \\ 5 x+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.415
5276	23564	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.415
5277	26676	\begin{align*} x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.415
5278	27672	\begin{align*} y^{\prime \prime }-y&=4 \sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.415
5279	333	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=2-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.416
5280	434	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.416
5281	7813	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.416
5282	20067	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x +{\mathrm e}^{m x} \\ \end{align*}	✓	✓	✓	✓	0.416
5283	26373	\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.416
5284	220	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.417
5285	1740	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= k_{0} \\ y^{\prime }\left (0\right ) &= k_{1} \\ \end{align*}	✓	✓	✓	✓	0.417
5286	2638	\begin{align*} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=2\).	✗	✗	✓	✗	0.417
5287	8681	\begin{align*} x^{\prime }+t&=1 \\ \end{align*}	✓	✓	✓	✓	0.417
5288	10197	\begin{align*} x^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.417
5289	14435	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 2 \\ y^{\prime \prime }\left (2\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.417
5290	15149	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.417
5291	15476	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.417
5292	16211	\begin{align*} y^{\prime }&=\sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	0.417
5293	17594	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=-\sec \left (t \right ) \tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.417
5294	19477	\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*}	✓	✓	✓	✓	0.417
5295	19509	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.417
5296	19584	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.417
5297	20865	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.417
5298	23447	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.417
5299	23450	\begin{align*} y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.417
5300	24026	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.417