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	11008	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
5202	13182	\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.352
5203	13733	\begin{align*} y^{\prime \prime } x +\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
5204	14583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5205	14928	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.352
5206	16580	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5207	17534	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5208	18198	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.352
5209	18652	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.352
5210	18688	\begin{align*} x^{\prime }&=-x-\frac {y}{2} \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.352
5211	22130	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.352
5212	23026	\begin{align*} y^{\prime \prime }-5 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5213	23028	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5214	23335	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5215	23364	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5216	24694	\begin{align*} 4 y+y^{\prime \prime }&=16 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.352
5217	25237	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.352
5218	429	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.353
5219	893	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.353
5220	1008	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.353
5221	2642	\begin{align*} t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.353
5222	3939	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.353
5223	6307	\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\ \end{align*}	✗	✗	✗	✗	0.353
5224	6475	\begin{align*} 2 y y^{\prime \prime }&=y^{2} \left (a x +b y\right )+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.353
5225	9719	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
5226	10061	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.353
5227	10384	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.353
5228	10751	\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.353
5229	16493	\begin{align*} 3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
5230	16582	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
5231	18049	\begin{align*} x^{2}+y^{\prime } x&=3 x +y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.353
5232	18662	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-5 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.353
5233	19246	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.353
5234	27684	\begin{align*} y^{\prime \prime }+y&=4 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.353
5235	27767	\begin{align*} \left (x^{2}-x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.353
5236	3292	\begin{align*} {y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5237	5377	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5238	9367	\begin{align*} y^{\prime }&=1+y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.354
5239	9468	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.354
5240	10446	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.354
5241	10612	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.354
5242	14964	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.354
5243	15706	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.354
5244	19058	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -5 \\ x_{2} \left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.354
5245	19380	\begin{align*} y^{\prime \prime }+2 x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5246	23110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5247	26413	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5248	27567	\begin{align*} y^{\prime \prime } x -y^{\prime }&=x^{2} y y^{\prime } \\ \end{align*}	✗	✓	✓	✗	0.354
5249	27671	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2^{x} \\ \end{align*}	✓	✓	✓	✓	0.354
5250	506	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
5251	658	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.355
5252	844	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.355
5253	892	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.355
5254	1270	\begin{align*} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
5255	1323	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
5256	1787	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	0.355
5257	2151	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.355
5258	2225	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 y^{\prime } x +24 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.355
5259	2370	\begin{align*} y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.355
5260	2621	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.355
5261	2733	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=4 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.355
5262	3938	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5263	7371	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
5264	7729	\begin{align*} 2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.355
5265	7981	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
5266	8150	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
5267	9612	\begin{align*} -y+y^{\prime }&=1+{\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5268	9633	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5269	13193	\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.355
5270	14601	\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.355
5271	14664	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.355
5272	14716	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.355
5273	15217	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5274	15249	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5275	15696	\begin{align*} 2 y+y^{\prime }&=4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5276	16673	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 x^{5} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.355
5277	16799	\begin{align*} y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
5278	19470	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
5279	20088	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.355
5280	20112	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.355
5281	20553	\begin{align*} x^{2} y^{\prime \prime \prime }-4 y^{\prime \prime } x +6 y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.355
5282	21656	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
5283	25229	\begin{align*} t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
5284	26196	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.355
5285	27643	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.355
5286	465	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
5287	880	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.356
5288	1005	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.356
5289	1069	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
5290	2829	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.356
5291	6847	\begin{align*} x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
5292	8490	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
5293	8845	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.356
5294	9493	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
5295	10463	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
5296	10555	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
5297	11141	\begin{align*} y^{\prime \prime } x +\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
5298	13183	\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.356
5299	15695	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.356
5300	15708	\begin{align*} y^{\prime }-2 y&=6 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.356