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	20922	\begin{align*} x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\ y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.426
5402	23442	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.426
5403	23662	\begin{align*} y^{\prime \prime \prime }+8 y&=-12 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= -8 \\ y^{\prime }\left (0\right ) &= 24 \\ y^{\prime \prime }\left (0\right ) &= -46 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.426
5404	23768	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.426
5405	24053	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.426
5406	636	\begin{align*} x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.427
5407	2422	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +\alpha ^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.427
5408	3423	\begin{align*} y^{\prime }&=\frac {t}{\sqrt {t}+1} \\ \end{align*}	✓	✓	✓	✓	0.427
5409	7216	\begin{align*} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.427
5410	13104	\begin{align*} x^{\prime }&=y-z \\ y^{\prime }&=x+y \\ z^{\prime }&=x+z \\ \end{align*}	✓	✓	✓	✓	0.427
5411	15574	\begin{align*} y^{\prime }&=\frac {1}{x -1} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.427
5412	20205	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&=0 \\ 5 x+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.427
5413	2287	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.428
5414	3200	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.428
5415	7651	\begin{align*} x^{\prime }+x \sin \left (t \right )&=0 \\ x \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.428
5416	8490	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5417	10583	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.428
5418	18679	\begin{align*} x^{\prime }&=-x+a y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.428
5419	21223	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.428
5420	22321	\begin{align*} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
5421	22883	\begin{align*} u^{\prime }&=2 v-1 \\ v^{\prime }&=1+2 u \\ \end{align*}	✓	✓	✓	✓	0.428
5422	23563	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.428
5423	23704	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5424	25184	\begin{align*} y^{\prime \prime }+\sqrt {y^{\prime }}+y&=t \\ \end{align*}	✗	✗	✗	✗	0.428
5425	628	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.429
5426	1403	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.429
5427	4033	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.429
5428	8938	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.429
5429	9347	\begin{align*} y^{\prime }&=2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.429
5430	9463	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.429
5431	15833	\begin{align*} \theta ^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.429
5432	18012	\begin{align*} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.429
5433	20993	\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.429
5434	23589	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.429
5435	23787	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.429
5436	4174	\begin{align*} y_{1}^{\prime }&=1 \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*}	✓	✓	✓	✓	0.430
5437	6497	\begin{align*} x y y^{\prime \prime }&=-y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.430
5438	7522	\begin{align*} y^{\prime }&=-4 x-y \\ x^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.430
5439	14381	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.430
5440	15573	\begin{align*} y^{\prime }&=x \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.430
5441	15687	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
5442	16043	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-2 y \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.430
5443	16045	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-4 y \\ z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
5444	16982	\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ \end{align*}	✓	✓	✓	✓	0.430
5445	20923	\begin{align*} x^{\prime }&=x-y+2 \cos \left (t \right ) \\ y^{\prime }&=x+y+3 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.430
5446	21743	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.430
5447	21777	\begin{align*} x^{\prime }&=2 x-7 y \\ y^{\prime }&=3 x-8 y \\ \end{align*}	✓	✓	✓	✓	0.430
5448	24711	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
5449	447	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ y \left (-3\right ) &= 0 \\ y^{\prime }\left (-3\right ) &= 2 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.431
5450	656	\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.431
5451	3343	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.431
5452	6505	\begin{align*} y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.431
5453	8969	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
5454	14052	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.431
5455	14762	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
5456	17698	\begin{align*} y^{\prime \prime }+\left (-1+y^{2}\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✗	0.431
5457	18428	\begin{align*} x^{\prime }&=8 y-x \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.431
5458	20015	\begin{align*} y&=y^{\prime } x +\frac {m}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	0.431
5459	21942	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
5460	22174	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.431
5461	23696	\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 \(x=0\).	✓	✓	✓	✓	0.431
5462	23707	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
5463	23711	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
5464	2052	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
5465	3925	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.432
5466	8493	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (-x +2\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
5467	8741	\begin{align*} y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.432
5468	15051	\begin{align*} y&=x^{2}+2 y^{\prime } x +\frac {{y^{\prime }}^{2}}{2} \\ \end{align*}	✓	✓	✗	✓	0.432
5469	15103	\begin{align*} -y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.432
5470	17863	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.432
5471	21032	\begin{align*} {\mathrm e}^{x^{\prime }}&=x \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	0.432
5472	22867	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
5473	22868	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
5474	1855	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.433
5475	2625	\begin{align*} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.433
5476	2773	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.433
5477	17901	\begin{align*} \tan \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.433
5478	22901	\begin{align*} x^{\prime }&=y+z \\ y^{\prime }&=x+z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.433
5479	1637	\begin{align*} y^{\prime } x +y&=y^{4} x^{4} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.434
5480	1682	\begin{align*} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.434
5481	3855	\begin{align*} x_{1}^{\prime }&=-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.434
5482	4028	\begin{align*} x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.434
5483	4534	\begin{align*} x^{\prime }-x+3 y&=0 \\ 3 x-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.434
5484	6317	\begin{align*} y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.434
5485	9683	\begin{align*} x^{\prime }&=\frac {x}{2} \\ y^{\prime }&=x-\frac {y}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.434
5486	12978	\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+y^{3} b x&=0 \\ \end{align*}	✗	✗	✗	✗	0.434
5487	14081	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.434
5488	15993	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.434
5489	19734	\begin{align*} {y^{\prime }}^{2} \left (x^{2}-1\right )&=1 \\ \end{align*}	✓	✓	✓	✓	0.434
5490	21213	\begin{align*} x^{\prime }&=3 x+t \\ y^{\prime }&=-y+2 t \\ \end{align*}	✓	✓	✓	✓	0.434
5491	23591	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.434
5492	23613	\begin{align*} x^{\prime }&=4 x+3 y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.434
5493	23714	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.434
5494	2699	\begin{align*} x^{\prime }&=6 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.435
5495	6328	\begin{align*} y^{\prime \prime }&=f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime } \\ \end{align*}	✗	✓	✗	✗	0.435
5496	9634	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.435
5497	14400	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=6 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.435
5498	17855	\begin{align*} y^{\prime }&=\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.435
5499	23571	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.435
5500	23811	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.435