2.3.107 Problems 10601 to 10700

Table 2.757: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10601	7766	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=4 \sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.747
10602	9950	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x -18 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.747
10603	16015	\begin{align*} x^{\prime }&=-3 x-5 y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.747
10604	17479	\begin{align*} x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.747
10605	23496	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.747
10606	26128	\begin{align*} x^{\prime }+x&=1 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.747
10607	1956	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.748
10608	6042	\begin{align*} -\left (-x^{2}+2\right ) y+x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.748
10609	15581	\begin{align*} y^{\prime }&=1-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.748
10610	17700	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.748
10611	18267	\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.748
10612	21681	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.748
10613	23448	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.748
10614	37	\begin{align*} y^{\prime }&=x +y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.749
10615	11739	\begin{align*} \left (x^{2}+a \right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}+b&=0 \\ \end{align*}	✓	✓	✓	✗	0.749
10616	12318	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.749
10617	16844	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.749
10618	23675	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.749
10619	25959	\begin{align*} y^{\prime \prime }+y^{\prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.749
10620	1454	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-2 \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.750
10621	2766	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\ \end{align*}	✓	✓	✓	✓	0.750
10622	6416	\begin{align*} f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime }&=g \left (y, f \left (x \right ) y^{\prime }\right ) \\ \end{align*}	✗	✗	✗	✗	0.750
10623	10448	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.750
10624	14872	\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	0.750
10625	15732	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2}+x -1 \\ y_{2}^{\prime }&=3 y_{1}+2 y_{2}-5 x -2 \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= -2 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.750
10626	17816	\begin{align*} x^{\prime \prime }+x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.750
10627	18107	\begin{align*} y^{\prime \prime }&=y^{\prime } \ln \left (y^{\prime }\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.750
10628	22937	\begin{align*} x^{\prime }+3 x-6 y&=0 \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.750
10629	25784	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.750
10630	9837	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.751
10631	10221	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.751
10632	12434	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.751
10633	18639	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x+2 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.751
10634	24571	\begin{align*} y^{\prime \prime }+y^{\prime }&=x +1 \\ y \left (0\right ) &= 1 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.751
10635	24732	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.751
10636	25555	\begin{align*} y^{\prime \prime }+5 y^{\prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	0.751
10637	3914	\begin{align*} x_{1}^{\prime }&=-6 x_{1}+x_{2}+1 \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.752
10638	6566	\begin{align*} A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.752
10639	8593	\begin{align*} 4 y^{\prime \prime } x +y^{\prime }+8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.752
10640	8618	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.752
10641	9563	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.752
10642	9676	\begin{align*} x^{\prime }&=x+y-z \\ y^{\prime }&=2 y \\ z^{\prime }&=y-z \\ \end{align*}	✓	✓	✓	✓	0.752
10643	16018	\begin{align*} x^{\prime }&=x+4 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.752
10644	16851	\begin{align*} y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.752
10645	17032	\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.752
10646	24589	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x}-x +\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.752
10647	3382	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.753
10648	4878	\begin{align*} x^{2} y^{\prime }&=a +b \,x^{n}+y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✗	0.753
10649	8063	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&=t \\ 5 x+y^{\prime }+3 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.753
10650	12465	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.753
10651	13017	\begin{align*} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.753
10652	19124	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.753
10653	17	\begin{align*} x^{\prime \prime }&=\frac {1}{\left (1+t \right )^{3}} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.754
10654	1978	\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*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.754
10655	4014	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.754
10656	4020	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (3 x +7\right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.754
10657	9573	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.754
10658	9693	\begin{align*} x^{\prime }&=5 x-4 y \\ y^{\prime }&=x+2 z \\ z^{\prime }&=2 y+5 z \\ \end{align*}	✓	✓	✓	✓	0.754
10659	20783	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✗	0.754
10660	23079	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.754
10661	3310	\begin{align*} x +2 y y^{\prime }&=x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.755
10662	4050	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.755
10663	6363	\begin{align*} y^{\prime \prime }&=a \left (b +c x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✗	✓	✓	✗	0.755
10664	6382	\begin{align*} -2 y^{\prime }+2 x {y^{\prime }}^{2}+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.755
10665	14623	\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=16 x -12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.755
10666	16942	\begin{align*} x^{\prime }&=8 x+2 y-17 \\ y^{\prime }&=4 x+y-13 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.755
10667	19054	\begin{align*} x_{1}^{\prime }&=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.755
10668	21564	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \\ \end{align*}	✓	✓	✓	✓	0.755
10669	22884	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.755
10670	23558	\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.755
10671	1852	\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*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.756
10672	5518	\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +4 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.756
10673	6228	\begin{align*} -6 y x +6 x^{2} y^{\prime }+\left (-2 x^{3}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.756
10674	9830	\begin{align*} x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.756
10675	10466	\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.756
10676	22722	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \left (1+\cos \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.756
10677	2014	\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757
10678	2735	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }&=3 x_{1}+3 x_{2}-x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.757
10679	4017	\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757
10680	5640	\begin{align*} {y^{\prime }}^{3}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+x y^{2} \left (y^{4}+x y^{2}+x^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	0.757
10681	6038	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.757
10682	8515	\begin{align*} 4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757
10683	9517	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757
10684	9522	\begin{align*} y^{\prime \prime }-4 y^{\prime } x -4 y&={\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.757
10685	9900	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.757
10686	12385	\begin{align*} y^{\prime \prime } x -2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x +2 a b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.757
10687	16930	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=1-2 x \\ \end{align*}	✓	✓	✓	✓	0.757
10688	19611	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757
10689	22924	\begin{align*} x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15 \\ 2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.757
10690	24727	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.757
10691	15879	\begin{align*} v^{\prime }&=-v^{2}-2 v-2 \\ \end{align*}	✓	✓	✓	✓	0.758
10692	17431	\begin{align*} y^{\prime \prime }+4 y&=4 \cos \left (t \right )-\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.758
10693	20162	\begin{align*} y^{\prime \prime }&=\frac {a}{x} \\ \end{align*}	✓	✓	✓	✓	0.758
10694	1750	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.759
10695	2019	\begin{align*} x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.759
10696	5995	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.759
10697	12332	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.759
10698	16887	\begin{align*} \left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.759
10699	17830	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.759
10700	21693	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✗	0.759