2.3.53 Problems 5201 to 5300

Table 2.649: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5201	10095	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.342
5202	12551	\begin{align*} 9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.342
5203	15111	\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*}	✓	✓	✓	✓	0.342
5204	16421	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.342
5205	18767	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5206	18890	\begin{align*} y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
5207	21586	\begin{align*} y^{\prime \prime }-y&=x^{2}-x +1 \\ \end{align*}	✓	✓	✓	✓	0.342
5208	21706	\begin{align*} y+y^{\prime }&=t \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
5209	22260	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }-y&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.342
5210	24541	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.342
5211	24660	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.342
5212	25632	\begin{align*} y^{\prime \prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
5213	26017	\begin{align*} y^{\prime \prime }-x -3 y x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.342
5214	856	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.343
5215	2213	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.343
5216	5510	\begin{align*} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
5217	8895	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.343
5218	9824	\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.343
5219	12899	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
5220	14102	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.343
5221	18156	\begin{align*} y^{\prime \prime }+y&=-\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.343
5222	18698	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.343
5223	18860	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.343
5224	19686	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.343
5225	24686	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 x^{3}-9 x^{2}+2 x -16 \\ \end{align*}	✓	✓	✓	✓	0.343
5226	24700	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.343
5227	24790	\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
5228	25081	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \cos \left (t \right )+\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.343
5229	589	\begin{align*} x^{\prime }&=-3 x+2 y \\ y^{\prime }&=-3 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.344
5230	590	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.344
5231	3285	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5232	6413	\begin{align*} \sqrt {x}\, y^{\prime \prime }&=y^{{3}/{2}} \\ \end{align*}	✗	✗	✗	✗	0.344
5233	6930	\begin{align*} 2 x +\cos \left (x \right ) y+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.344
5234	7459	\begin{align*} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5235	7720	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.344
5236	8821	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.344
5237	10096	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2&=0 \\ \end{align*}	✓	✓	✓	✗	0.344
5238	15267	\begin{align*} x^{\prime }-x+2 y&=0 \\ y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5239	16771	\begin{align*} t y^{\prime \prime }+y^{\prime }+t y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.344
5240	18158	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.344
5241	18200	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\left (x^{2}+x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.344
5242	21517	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.344
5243	22486	\begin{align*} y^{\prime \prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5244	23397	\begin{align*} x y^{\prime \prime \prime }-\frac {6 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
5245	506	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
5246	631	\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*}	✓	✓	✓	✓	0.345
5247	968	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.345
5248	3506	\begin{align*} y^{\prime \prime }-2 z y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.345
5249	3881	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.345
5250	3996	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
5251	4160	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.345
5252	5508	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
5253	8492	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
5254	9178	\begin{align*} x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
5255	10094	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.345
5256	10102	\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.345
5257	15265	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.345
5258	17367	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.345
5259	18389	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
5260	18689	\begin{align*} x^{\prime }&=2 x+\frac {y}{2} \\ y^{\prime }&=-\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.345
5261	24546	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \cos \left (x \right )+4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.345
5262	25119	\begin{align*} y^{\prime \prime }-y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.345
5263	966	\begin{align*} x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.346
5264	1461	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.346
5265	3112	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.346
5266	4377	\begin{align*} \left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
5267	6136	\begin{align*} -2 \left (1-3 x \right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
5268	6475	\begin{align*} 2 y y^{\prime \prime }&=y^{2} \left (a x +b y\right )+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.346
5269	7590	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
5270	8894	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.346
5271	14126	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.346
5272	16148	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.346
5273	18919	\begin{align*} y_{1}^{\prime }&=-2 y_{1}+y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.346
5274	20520	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
5275	20892	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.346
5276	22149	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.346
5277	24437	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.346
5278	24545	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=20 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.346
5279	25082	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.346
5280	25084	\begin{align*} y^{\prime \prime }-3 y&=4 t^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.346
5281	387	\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.347
5282	628	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.347
5283	656	\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.347
5284	1371	\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.347
5285	8192	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}	✓	✓	✓	✓	0.347
5286	8197	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=5 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.347
5287	13157	\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.347
5288	14571	\begin{align*} \left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.347
5289	16056	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.347
5290	25553	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	0.347
5291	26037	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.347
5292	351	\begin{align*} 4 y+y^{\prime \prime }&=2 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.348
5293	1368	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.348
5294	1786	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\ y \left (-1\right ) &= 7 \\ y^{\prime }\left (-1\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.348
5295	2256	\begin{align*} y_{1}^{\prime }&=3 y_{1}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+y_{2} \\ \end{align*}	✓	✓	✓	✓	0.348
5296	8129	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.348
5297	8855	\begin{align*} y^{\prime }&={\mathrm e}^{3 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.348
5298	9444	\begin{align*} y^{\prime \prime }-y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.348
5299	10553	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
5300	10566	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348