2.3.48 Problems 4701 to 4800

Table 2.669: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4701	1856	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.592
4702	2703	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.592
4703	2739	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.592
4704	2753	\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+3 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.592
4705	3818	\begin{align*} x_{1}^{\prime }&=2 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.592
4706	7591	\begin{align*} y^{\prime \prime }-y^{\prime }-11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.592
4707	18690	\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.592
4708	872	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.593
4709	1317	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.593
4710	1863	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.593
4711	3346	\begin{align*} y^{\prime \prime }&=\sin \left (y\right ) \\ y \left (0\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.593
4712	4136	\begin{align*} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.593
4713	10507	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.593
4714	19468	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.593
4715	873	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.594
4716	1314	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.594
4717	3114	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.594
4718	3178	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.594
4719	3892	\begin{align*} x_{1}^{\prime }&=-6 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.594
4720	7820	\begin{align*} 2 y+y^{\prime }&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.594
4721	9307	\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}	✓	✓	✓	✓	0.594
4722	12954	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	0.594
4723	22746	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \\ \end{align*}	✓	✓	✓	✓	0.594
4724	344	\begin{align*} 4 y+y^{\prime \prime }&=3 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
4725	385	\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.595
4726	2717	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
4727	3429	\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\ y \left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	0.595
4728	6930	\begin{align*} 2 x +\cos \left (x \right ) y+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.595
4729	8930	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.595
4730	10511	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.595
4731	10838	\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.595
4732	19463	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.595
4733	21191	\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.595
4734	594	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=x+2 y-{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.596
4735	914	\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.596
4736	3872	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{2}+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.596
4737	10510	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.596
4738	10939	\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.596
4739	17686	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.596
4740	18919	\begin{align*} y_{1}^{\prime }&=-2 y_{1}+y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.596
4741	1776	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.597
4742	2279	\begin{align*} y_{1}^{\prime }&=2 y_{2}-2 y_{3} \\ y_{2}^{\prime }&=-y_{1}+5 y_{2}-3 y_{3} \\ y_{3}^{\prime }&=y_{1}+y_{2}+y_{3} \\ \end{align*}	✓	✓	✓	✓	0.597
4743	9215	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.597
4744	12800	\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.597
4745	453	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
4746	1337	\begin{align*} y^{\prime \prime }+y&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.598
4747	1879	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
4748	18228	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.598
4749	18451	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.598
4750	584	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=13 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.599
4751	856	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.599
4752	1818	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=6 \,{\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.599
4753	1866	\begin{align*} \left (8 x^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.599
4754	2401	\begin{align*} y^{\prime \prime }+y&=\sec \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
4755	9029	\begin{align*} 3 \ln \left (x \right ) x^{2}+x^{2}+y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.599
4756	12633	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.599
4757	14376	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.599
4758	18081	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.599
4759	21665	\begin{align*} x^{\prime }+x^{2}&=0 \\ x \left (-\frac {1}{2}\right ) &= 0 \\ \end{align*} Series expansion around \(t=-{\frac {1}{2}}\).	✓	✓	✓	✓	0.599
4760	23406	\begin{align*} x^{3} y^{\prime \prime }+\left (5 x^{3}-x^{2}\right ) y^{\prime }+2 \left (3 x^{3}-x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.599
4761	24683	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.599
4762	2398	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.601
4763	2800	\begin{align*} x^{\prime }&=-5 x+3 y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.601
4764	7061	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.601
4765	17831	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.601
4766	18917	\begin{align*} y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= -3 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.601
4767	19647	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.601
4768	19686	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.601
4769	20112	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.601
4770	23422	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.601
4771	2382	\begin{align*} 2 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.602
4772	7233	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.602
4773	26783	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+12 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.602
4774	1411	\begin{align*} x_{1}^{\prime }&=\frac {3 x_{1}}{4}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{4} \\ \end{align*}	✓	✓	✓	✓	0.603
4775	1412	\begin{align*} x_{1}^{\prime }&=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}+\frac {6 x_{2}}{5} \\ \end{align*}	✓	✓	✓	✓	0.603
4776	3176	\begin{align*} y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.603
4777	7043	\begin{align*} 6 y^{\prime \prime }-11 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.603
4778	14993	\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.603
4779	18452	\begin{align*} x^{\prime }&=6 x+y \\ y^{\prime }&=4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.603
4780	865	\begin{align*} 2 x^{\prime \prime }+12 x^{\prime }+50 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.604
4781	1409	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.604
4782	3741	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.604
4783	21571	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
4784	24036	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
4785	864	\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.605
4786	983	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.605
4787	2278	\begin{align*} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3} \\ \end{align*}	✓	✓	✓	✓	0.605
4788	2755	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.605
4789	5919	\begin{align*} -\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.605
4790	12369	\begin{align*} y^{\prime \prime } x -2 y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
4791	17298	\begin{align*} y^{\prime } t -{y^{\prime }}^{3}&=y \\ \end{align*}	✓	✓	✓	✗	0.605
4792	17697	\begin{align*} y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.605
4793	17752	\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}	✓	✓	✓	✓	0.605
4794	21180	\begin{align*} x^{\prime \prime \prime }+4 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ x^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.605
4795	22093	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
4796	26493	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
4797	513	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.606
4798	867	\begin{align*} 2 x^{\prime \prime }+16 x^{\prime }+40 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.606
4799	1032	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.606
4800	1807	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=3 \,{\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.606