2.3.53 Problems 5201 to 5300

Table 2.637: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5201	24704	\begin{align*} 4 y+y^{\prime \prime }&=8 \cos \left (x \right ) \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.274
5202	25102	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.274
5203	25105	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.274
5204	25591	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.274
5205	25597	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.274
5206	4168	\begin{align*} y_{1}^{\prime }&=4 y_{2} \\ y_{2}^{\prime }&=4 y_{2}-y_{1} \\ \end{align*}	✓	✓	✓	✓	0.275
5207	10968	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.275
5208	19476	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.275
5209	20089	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=20 x \\ \end{align*}	✓	✓	✓	✓	0.275
5210	20913	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.275
5211	22578	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.275
5212	22624	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.275
5213	23785	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.275
5214	220	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.276
5215	3710	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.276
5216	3829	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{2}-x_{1} \\ \end{align*}	✓	✓	✓	✓	0.276
5217	5404	\begin{align*} {y^{\prime }}^{2}-a x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
5218	6241	\begin{align*} \left (2 x +1\right ) y-2 x^{2} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
5219	6530	\begin{align*} \operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.276
5220	7828	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.276
5221	7899	\begin{align*} -y-3 x^{2} \left (y^{2}+x^{2}\right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
5222	8714	\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.276
5223	10469	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
5224	10547	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
5225	10907	\begin{align*} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
5226	13164	\(\left [\begin {array}{cc} 0 & 1 \\ -1 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.276
5227	13934	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
5228	15494	\begin{align*} y^{\prime } x -\sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
5229	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*}	✓	✓	✓	✓	0.276
5230	16162	\begin{align*} y^{\prime }&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.276
5231	23812	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-3 y \\ \end{align*}	✓	✓	✓	✓	0.276
5232	24644	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.276
5233	24748	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.276
5234	25587	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.276
5235	25599	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.276
5236	1271	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -\beta \\ \end{align*}	✓	✓	✓	✗	0.277
5237	1379	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.277
5238	3894	\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.277
5239	4254	\begin{align*} \cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
5240	7366	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.277
5241	7843	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.277
5242	8281	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.277
5243	10359	\begin{align*} y^{\prime } x +y&=\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.277
5244	10711	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
5245	11068	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
5246	11147	\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 y x}{16}&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
5247	11207	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
5248	14286	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.277
5249	15082	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
5250	15159	\begin{align*} y^{\prime \prime }+\frac {k x}{y^{4}}&=0 \\ \end{align*}	✗	✓	✗	✗	0.277
5251	16020	\begin{align*} x^{\prime }&=-3 x+10 y \\ y^{\prime }&=-x+3 y \\ \end{align*}	✓	✓	✓	✓	0.277
5252	21971	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.277
5253	22304	\begin{align*} y^{\prime }&=3 \sin \left (x \right ) \\ y \left (\pi \right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.277
5254	24652	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.277
5255	24788	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (y-x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
5256	2555	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
5257	6223	\begin{align*} -2 y+\left (1-x \right )^{2} x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
5258	7837	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.278
5259	9368	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.278
5260	10655	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
5261	10925	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
5262	16363	\begin{align*} \left (2+x \right ) y^{\prime }-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
5263	17351	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
5264	18684	\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.278
5265	21082	\begin{align*} y^{2}+\left (y x +3 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
5266	21712	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.278
5267	23784	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.278
5268	24678	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2}+3 x +3 \\ \end{align*}	✓	✓	✓	✓	0.278
5269	25569	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.278
5270	375	\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.279
5271	1372	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
5272	1635	\begin{align*} y^{\prime }-2 y&=x y^{3} \\ y \left (0\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	0.279
5273	3856	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.279
5274	3992	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
5275	4590	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
5276	5800	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.279
5277	6356	\begin{align*} y^{\prime \prime }&=A \,x^{a} y^{b} {y^{\prime }}^{c} \\ \end{align*}	✗	✗	✗	✗	0.279
5278	8101	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
5279	10504	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.279
5280	10794	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.279
5281	15827	\begin{align*} y^{\prime }&=-t^{2}+2 \\ \end{align*}	✓	✓	✓	✓	0.279
5282	18761	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
5283	20343	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.279
5284	22185	\begin{align*} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.279
5285	22492	\begin{align*} y^{\prime \prime \prime \prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.279
5286	22753	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.279
5287	22783	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.279
5288	23690	\begin{align*} y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+4 y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.279
5289	23781	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.279
5290	24540	\begin{align*} 4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.279
5291	24935	\begin{align*} y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	0.279
5292	5	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {2+x}} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.280
5293	443	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.280
5294	450	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.280
5295	1363	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.280
5296	1762	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.280
5297	1797	\begin{align*} 36 y^{\prime }+36 y^{2}-12 y+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
5298	3404	\begin{align*} y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\ \end{align*}	✓	✓	✓	✓	0.280
5299	3884	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.280
5300	6376	\begin{align*} a \,x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.280