2.3.55 Problems 5401 to 5500

Table 2.641: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5401	23770	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.284
5402	24031	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.284
5403	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*}	✓	✓	✓	✓	0.285
5404	3407	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.285
5405	5683	\begin{align*} \left (x -y\right ) \sqrt {y^{\prime }}&=a \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	0.285
5406	8016	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.285
5407	8575	\begin{align*} y^{\prime }+4 y&=1 \\ y \left (0\right ) &= {\frac {5}{4}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.285
5408	10548	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
5409	12771	\begin{align*} 4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	0.285
5410	20912	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.285
5411	22827	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.285
5412	23006	\begin{align*} y^{\prime \prime }-2 y^{\prime }-63 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.285
5413	23804	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.285
5414	24680	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+6 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.285
5415	24882	\begin{align*} y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\ y \left (2\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	0.285
5416	24932	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.285
5417	25269	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.285
5418	247	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5419	448	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
5420	1272	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \beta \\ \end{align*}	✓	✓	✓	✗	0.286
5421	1374	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
5422	1637	\begin{align*} y^{\prime } x +y&=y^{4} x^{4} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.286
5423	2223	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.286
5424	2556	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5425	2558	\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5426	6024	\begin{align*} \left (b +c \,x^{2 k}\right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5427	6377	\begin{align*} b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.286
5428	8055	\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5429	8744	\begin{align*} 2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5430	9366	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
5431	9467	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.286
5432	9495	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
5433	10642	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5434	10990	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5435	11069	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5436	12599	\begin{align*} y^{\prime \prime }&=-\frac {\left (1-3 x \right ) y}{\left (x -1\right ) \left (2 x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.286
5437	13168	\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.286
5438	14322	\begin{align*} x^{\prime \prime }&=\frac {4 x}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.286
5439	15415	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5440	16719	\begin{align*} x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5441	17392	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5442	17740	\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5443	18085	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.286
5444	19021	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.286
5445	20558	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5446	20649	\begin{align*} \left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.286
5447	20712	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
5448	22130	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.286
5449	22801	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5450	23769	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.286
5451	24087	\begin{align*} \left (x^{3}-8\right ) y^{\prime \prime }-4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
5452	24550	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.286
5453	24804	\begin{align*} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
5454	2424	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.287
5455	3582	\begin{align*} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\ \end{align*}	✓	✓	✓	✓	0.287
5456	6852	\begin{align*} {\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
5457	7972	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.287
5458	7987	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.287
5459	8088	\begin{align*} z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.287
5460	9274	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.287
5461	9347	\begin{align*} y^{\prime }&=2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.287
5462	10514	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
5463	10608	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
5464	10964	\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
5465	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*}	✓	✓	✓	✓	0.287
5466	16565	\begin{align*} 4 x^{2} y^{\prime \prime }+37 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
5467	16826	\begin{align*} y^{\prime }+\frac {y}{x -1}&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.287
5468	19768	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
5469	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*}	✓	✓	✓	✗	0.287
5470	23049	\begin{align*} x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.287
5471	23317	\begin{align*} 3 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
5472	23506	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.287
5473	2221	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=2 x \\ \end{align*}	✓	✓	✓	✓	0.288
5474	6467	\begin{align*} 2 y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.288
5475	7806	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.288
5476	8610	\begin{align*} y^{\prime \prime }+k^{2} x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.288
5477	8940	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.288
5478	10565	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.288
5479	10723	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.288
5480	14387	\begin{align*} x^{\prime }&=-6 y \\ y^{\prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	0.288
5481	14716	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.288
5482	16982	\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ \end{align*}	✓	✓	✓	✓	0.288
5483	21280	\begin{align*} x^{\prime }+x&={\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.288
5484	21974	\begin{align*} y^{\prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.288
5485	22149	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.288
5486	22732	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.288
5487	23065	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.288
5488	23693	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.288
5489	24473	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.288
5490	24627	\begin{align*} y^{\prime \prime }-9 y&=18 x -162 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.288
5491	1383	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.289
5492	2851	\begin{align*} x^{\prime }&=1-\sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.289
5493	3087	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.289
5494	5408	\begin{align*} {y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.289
5495	5465	\begin{align*} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5496	7631	\begin{align*} y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.289
5497	7906	\begin{align*} y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5498	8795	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=1+3 x \\ \end{align*}	✓	✓	✓	✓	0.289
5499	9112	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✗	✗	✓	0.289
5500	9331	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.289