2.3.187 Problems 18601 to 18700

Table 2.947: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18601	13972	\begin{align*} \left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.821
18602	4951	\begin{align*} 2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.822
18603	6869	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-\frac {2 a}{3}} \\ \end{align*}	✓	✓	✓	✗	2.822
18604	16492	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.822
18605	8454	\begin{align*} y^{\prime }-\sin \left (x \right ) y&=2 \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.823
18606	7749	\begin{align*} y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.824
18607	3541	\begin{align*} y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\ \end{align*}	✓	✓	✓	✓	2.825
18608	9083	\begin{align*} y^{\prime }&=4 y x \\ \end{align*}	✓	✓	✓	✓	2.825
18609	20268	\begin{align*} y-x \sin \left (x^{2}\right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.825
18610	1210	\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.826
18611	25905	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\ \end{align*}	✓	✓	✓	✓	2.826
18612	2304	\begin{align*} \frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \\ \end{align*}	✓	✓	✓	✗	2.827
18613	17185	\begin{align*} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.827
18614	18585	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.827
18615	22933	\begin{align*} z+x^{\prime }&=x \\ y^{\prime }-2 x&=y+3 t \\ z^{\prime }+4 y&=z-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.828
18616	25056	\begin{align*} y^{\prime } t&=2 y-t \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✗	✓	✓	2.828
18617	25474	\begin{align*} y^{\prime }&=a y-b y^{n} \\ \end{align*}	✓	✓	✓	✗	2.828
18618	5075	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	2.829
18619	15372	\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.829
18620	3027	\begin{align*} 3 x -6&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	2.832
18621	17782	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.832
18622	25298	\begin{align*} y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.832
18623	14290	\begin{align*} x^{\prime \prime }-12 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.833
18624	17657	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.833
18625	11719	\begin{align*} \left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0}&=0 \\ \end{align*}	✓	✗	✓	✗	2.834
18626	15484	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.834
18627	20278	\begin{align*} 1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.834
18628	7426	\begin{align*} r^{\prime }+r \tan \left (\theta \right )&=\sec \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.835
18629	8502	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.836
18630	22040	\begin{align*} y^{\prime }&=\frac {-y+x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	2.836
18631	23954	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{3} x \\ \end{align*}	✓	✓	✓	✓	2.836
18632	9050	\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	2.837
18633	15635	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.837
18634	2842	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.838
18635	11583	\begin{align*} \left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 y x +a&=0 \\ \end{align*}	✓	✓	✓	✓	2.838
18636	24867	\begin{align*} {y^{\prime }}^{2}+y y^{\prime }-x -1&=0 \\ \end{align*}	✓	✓	✓	✗	2.838
18637	24261	\begin{align*} \left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.839
18638	5220	\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	2.840
18639	22576	\begin{align*} \left ({\mathrm e}^{y}+x +3\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.841
18640	8345	\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}	✓	✓	✓	✓	2.842
18641	16233	\begin{align*} y^{\prime }&=200 y-2 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.842
18642	19972	\begin{align*} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.842
18643	25017	\begin{align*} y y^{\prime }+t y^{2}&=t \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.842
18644	12449	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-x^{2} \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.843
18645	1541	\begin{align*} x^{2} y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.845
18646	17374	\begin{align*} t^{2} y^{\prime \prime }+a t y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	2.845
18647	7539	\begin{align*} y^{\prime }+\tan \left (x \right ) y+\sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.846
18648	17356	\begin{align*} 3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\ \end{align*}	✓	✓	✓	✓	2.846
18649	18108	\begin{align*} y^{\prime \prime }+y^{\prime }+2&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.846
18650	19679	\begin{align*} x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.847
18651	21671	\begin{align*} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.848
18652	195	\begin{align*} {\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.849
18653	9553	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.849
18654	16552	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.849
18655	17672	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.849
18656	15562	\begin{align*} y^{\prime }&=y x +\frac {1}{x^{2}+1} \\ y \left (-5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.850
18657	19267	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.850
18658	19128	\begin{align*} y^{\prime }&=\sqrt {-x +y}+1 \\ \end{align*}	✓	✓	✓	✓	2.851
18659	4714	\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.852
18660	5730	\begin{align*} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.852
18661	7747	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.852
18662	15893	\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.852
18663	15952	\begin{align*} y^{\prime }&=2 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.852
18664	17879	\begin{align*} 1+y^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	2.852
18665	24244	\begin{align*} y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.852
18666	5215	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.853
18667	17414	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.853
18668	15783	\begin{align*} y^{\prime }&=\frac {t}{y+t^{2} y} \\ \end{align*}	✓	✓	✓	✓	2.854
18669	17457	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=18 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.854
18670	3003	\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.855
18671	25500	\begin{align*} y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.855
18672	1545	\begin{align*} y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.856
18673	1689	\begin{align*} 2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.856
18674	20005	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.857
18675	21058	\begin{align*} x^{\prime }&=-\frac {t}{4 x^{3}} \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.857
18676	15410	\begin{align*} y^{\prime \prime }&=9 y \\ \end{align*}	✓	✓	✓	✓	2.858
18677	20060	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.858
18678	6892	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\ \end{align*}	✓	✓	✓	✓	2.859
18679	14241	\begin{align*} y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.859
18680	17171	\begin{align*} x^{\prime }&=x+t +1 \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.859
18681	23201	\begin{align*} 2 x^{2}+2 y^{2}+x +\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.859
18682	27296	\begin{align*} x^{\prime }+x&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.859
18683	5549	\begin{align*} y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.860
18684	15907	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.860
18685	23274	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.860
18686	5463	\begin{align*} x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.861
18687	5540	\begin{align*} x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.861
18688	7675	\begin{align*} y^{\prime }-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	2.861
18689	11636	\begin{align*} \left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.861
18690	21790	\begin{align*} y^{\prime } x&=x +2 y \\ \end{align*}	✓	✓	✓	✓	2.861
18691	1613	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	2.862
18692	5715	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.862
18693	15018	\begin{align*} y^{\prime } x +y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	2.862
18694	19730	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.862
18695	1105	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.863
18696	3019	\begin{align*} r^{\prime }&=r \cot \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.864
18697	22011	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.864
18698	4195	\begin{align*} y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	2.865
18699	4635	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\ \end{align*}	✓	✓	✓	✗	2.866
18700	8251	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.867