2.3.55 Problems 5401 to 5500

Table 2.683: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5401	15486	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.424
5402	15831	\begin{align*} y^{\prime }&=t^{2}-2 \\ \end{align*}	✓	✓	✓	✓	0.424
5403	15997	\begin{align*} x^{\prime }&=-2 x-2 y \\ y^{\prime }&=-2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.424
5404	16070	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.424
5405	16615	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \\ \end{align*}	✓	✓	✓	✓	0.424
5406	17022	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.424
5407	20102	\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}	✓	✓	✓	✓	0.424
5408	20386	\begin{align*} y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.424
5409	21280	\begin{align*} x^{\prime }+x&={\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.424
5410	21726	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.424
5411	25370	\begin{align*} y_{1}^{\prime }&=2 y_{1}+y_{2} \\ y_{2}^{\prime }&=2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= -1 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.424
5412	26985	\begin{align*} y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.424
5413	27183	\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2} \\ x_{2}^{\prime }&=-5 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.424
5414	27728	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.424
5415	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*}	✓	✓	✓	✓	0.425
5416	3881	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.425
5417	4377	\begin{align*} \left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
5418	4519	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.425
5419	6699	\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
5420	8339	\begin{align*} y^{\prime }&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.425
5421	8964	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.425
5422	8966	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.425
5423	10365	\begin{align*} a {y^{\prime \prime }}^{n}&=0 \\ \end{align*}	✓	✓	✓	✗	0.425
5424	10929	\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.425
5425	15994	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=x-4 y \\ \end{align*}	✓	✓	✓	✓	0.425
5426	16719	\begin{align*} x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
5427	21984	\begin{align*} y x +y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
5428	23066	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.425
5429	24924	\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.425
5430	25105	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
5431	26134	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=-5 x-y \\ \end{align*}	✓	✓	✓	✓	0.425
5432	27786	\begin{align*} x y^{\prime }&=x^{2} \mu +\ln \left (y\right ) \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.425
5433	1855	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.426
5434	2377	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.426
5435	6936	\begin{align*} y^{2}+y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.426
5436	11323	\begin{align*} y^{\prime }-y^{2}+y \sin \left (x \right )-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.426
5437	16031	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.426
5438	16848	\begin{align*} y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.426
5439	17851	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.426
5440	19656	\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}	✓	✓	✓	✓	0.426
5441	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*}	✓	✓	✓	✓	0.426
5442	3186	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.427
5443	8632	\begin{align*} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {63}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.427
5444	10338	\begin{align*} t y^{\prime }+y&=0 \\ y \left (1\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.427
5445	11067	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.427
5446	17423	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	0.427
5447	19208	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.427
5448	20132	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.427
5449	20924	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.427
5450	23068	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.427
5451	23594	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=9 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.427
5452	24116	\begin{align*} y^{\prime }&=x +2 y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.427
5453	1073	\begin{align*} \left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5454	1284	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.428
5455	1879	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5456	1929	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5457	2255	\begin{align*} y_{1}^{\prime }&=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-11 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.428
5458	2549	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.428
5459	2776	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.428
5460	3407	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.428
5461	6715	\begin{align*} -y+x y^{\prime }+4 x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
5462	7132	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
5463	7574	\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
5464	7838	\begin{align*} y^{\prime \prime }-2 x y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5465	9035	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.428
5466	9992	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.428
5467	10413	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.428
5468	12837	\begin{align*} y^{\prime \prime }-6 y^{2}-x&=0 \\ \end{align*}	✗	✗	✗	✗	0.428
5469	14009	\begin{align*} x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
5470	14633	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.428
5471	15012	\begin{align*} x^{\prime }&=13 x \\ y^{\prime }&=13 y \\ \end{align*}	✓	✓	✓	✓	0.428
5472	16838	\begin{align*} 6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5473	16953	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.428
5474	17685	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
5475	19422	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x \\ \end{align*}	✓	✓	✓	✓	0.428
5476	19482	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.428
5477	21299	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
5478	23928	\begin{align*} 6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.428
5479	26930	\begin{align*} y^{\prime \prime }+36 y&=x -1 \\ \end{align*}	✓	✓	✓	✓	0.428
5480	1714	\begin{align*} 2 y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
5481	2827	\begin{align*} x_{1}^{\prime }&=-4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-6 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.429
5482	10061	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.429
5483	13668	\begin{align*} y^{\prime \prime }-a \,x^{n} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.429
5484	17641	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.429
5485	17833	\begin{align*} x^{\prime \prime }-3 x^{\prime }+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
5486	20388	\begin{align*} x +y {y^{\prime }}^{2}&=\left (y x +1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.429
5487	21639	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.429
5488	26740	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.429
5489	27576	\begin{align*} x^{2} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=y^{2} \\ \end{align*}	✗	✓	✓	✗	0.429
5490	974	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.430
5491	1402	\begin{align*} x_{1}^{\prime }&=-x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.430
5492	1403	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.430
5493	9827	\begin{align*} {y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
5494	13195	\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.430
5495	15766	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.430
5496	16110	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
5497	16834	\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.430
5498	20344	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=15 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.430
5499	23512	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.430
5500	23823	\begin{align*} x^{\prime }&=-3 x+2 y \\ y^{\prime }&=-2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.430