2.3.197 Problems 19601 to 19700

Table 2.937: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19601	19228	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	4.720
19602	7162	\begin{align*} \sin \left (x \right ) \cos \left (y\right )&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.722
19603	19308	\begin{align*} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.723
19604	5001	\begin{align*} x^{5} y^{\prime }&=1-3 x^{4} y \\ \end{align*}	✓	✓	✓	✓	4.724
19605	14510	\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	4.726
19606	11965	\begin{align*} y^{\prime }&=\frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	4.728
19607	5517	\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	4.729
19608	25840	\begin{align*} \left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.729
19609	15625	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.730
19610	19401	\begin{align*} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.730
19611	9136	\begin{align*} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.732
19612	11488	\begin{align*} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	4.734
19613	12060	\begin{align*} y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	4.734
19614	14280	\begin{align*} x^{\prime \prime }-2 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.734
19615	4972	\begin{align*} x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.735
19616	4428	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.736
19617	19076	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.736
19618	2960	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	4.737
19619	7427	\begin{align*} y^{\prime } x +2 y&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	4.739
19620	15790	\begin{align*} y^{\prime }&=\frac {1}{t y+t +y+1} \\ \end{align*}	✓	✓	✓	✓	4.740
19621	17315	\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.741
19622	4940	\begin{align*} x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.743
19623	12295	\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	4.743
19624	9198	\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.745
19625	15622	\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.749
19626	17058	\begin{align*} \left (-2+t \right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	4.750
19627	24378	\begin{align*} y^{2}-3 y-x +\left (2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.752
19628	2930	\begin{align*} 2 y \sin \left (y x \right )+\left (2 x \sin \left (y x \right )+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.753
19629	7567	\begin{align*} y^{\prime }&=2 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.753
19630	1646	\begin{align*} x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	4.754
19631	22027	\begin{align*} 2 y x +x +\left (y+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.755
19632	23836	\begin{align*} y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	4.755
19633	1153	\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.756
19634	23382	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.761
19635	25721	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.761
19636	13261	\begin{align*} \left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 y x +\left (1-a \right ) x^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✗	4.762
19637	17024	\begin{align*} y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.762
19638	19356	\begin{align*} y^{\prime } x&=2 x^{2} y+y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.762
19639	5269	\begin{align*} 3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 y x -2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.763
19640	11781	\begin{align*} \left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +\left (-a^{2}+1\right ) x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.763
19641	20037	\begin{align*} y^{\prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.763
19642	20298	\begin{align*} \left (x -y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	4.763
19643	7404	\begin{align*} y^{\prime }&=x^{2} \left (1+y\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.765
19644	21456	\begin{align*} y^{\prime }+y&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	4.765
19645	21620	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= v \\ \end{align*}	✓	✓	✓	✓	4.765
19646	5217	\begin{align*} \left (1-x^{2}+y^{2}\right ) y^{\prime }&=-y^{2}+x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	4.766
19647	4323	\begin{align*} y^{\prime }&=\sin \left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.767
19648	8347	\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	4.767
19649	14108	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.767
19650	5683	\begin{align*} \left (x -y\right ) \sqrt {y^{\prime }}&=a \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	4.773
19651	16301	\begin{align*} \left (-x +y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	4.773
19652	24293	\begin{align*} y-\sin \left (x \right )^{2}+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.774
19653	14487	\begin{align*} y^{\prime } x +\frac {\left (2 x +1\right ) y}{x +1}&=x -1 \\ \end{align*}	✓	✓	✓	✓	4.776
19654	14900	\begin{align*} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	4.776
19655	4869	\begin{align*} x^{2} y^{\prime }&=\left (b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	4.777
19656	6492	\begin{align*} 12 y y^{\prime \prime }&=-8 y^{3}+15 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.778
19657	17161	\begin{align*} p^{\prime }&=t^{3}+\frac {p}{t} \\ \end{align*}	✓	✓	✓	✓	4.778
19658	19312	\begin{align*} 3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.782
19659	5314	\begin{align*} \left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \\ \end{align*}	✓	✓	✓	✓	4.783
19660	11497	\begin{align*} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.790
19661	16312	\begin{align*} y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \\ \end{align*}	✓	✓	✓	✓	4.790
19662	4437	\begin{align*} y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.793
19663	22092	\begin{align*} y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.793
19664	22997	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✓	4.794
19665	25875	\begin{align*} y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.794
19666	15257	\begin{align*} y^{\prime \prime }+y^{\prime } t -y \ln \left (t \right )&=\cos \left (2 t \right ) \\ \end{align*}	✗	✗	✗	✗	4.796
19667	2977	\begin{align*} y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.797
19668	5836	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	4.798
19669	19305	\begin{align*} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.798
19670	4246	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.800
19671	3644	\begin{align*} 2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.802
19672	13272	\begin{align*} \left (a \,x^{2}+b x +e \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.802
19673	22219	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.802
19674	4309	\begin{align*} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.803
19675	11939	\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \\ \end{align*}	✓	✓	✓	✓	4.803
19676	17073	\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✗	4.804
19677	6319	\begin{align*} y^{\prime \prime }&=f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime } \\ \end{align*}	✗	✓	✗	✗	4.807
19678	17934	\begin{align*} \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=2 x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.809
19679	17968	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.809
19680	21348	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	4.810
19681	24843	\begin{align*} y {y^{\prime }}^{3}-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.810
19682	7704	\begin{align*} y^{\prime } x -2 y&=x^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.816
19683	2337	\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.817
19684	16375	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.818
19685	24215	\begin{align*} x^{3}+x y^{2}+y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.819
19686	2847	\begin{align*} \left (x +1\right ) y^{\prime }-1+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.820
19687	14488	\begin{align*} \left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y&=x -1 \\ \end{align*}	✓	✓	✓	✓	4.822
19688	15374	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.822
19689	24959	\begin{align*} y^{3} y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	4.822
19690	25504	\begin{align*} \left (1+t \right ) y^{\prime }&=4 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.822
19691	24997	\begin{align*} y^{\prime } t +2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.823
19692	26221	\begin{align*} x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.824
19693	26097	\begin{align*} y^{\prime \prime }&=18 y^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	4.826
19694	17166	\begin{align*} 2 t y+y^{\prime }&=2 t \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.828
19695	3022	\begin{align*} y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.829
19696	3774	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.829
19697	4301	\begin{align*} x \left (x -1\right ) y^{\prime }&=\cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.830
19698	7736	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=\cos \left (x \right )-2 x \sin \left (x \right ) \\ y \left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.830
19699	106	\begin{align*} 2 y y^{\prime } x&=x^{2}+2 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.832
19700	6353	\begin{align*} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.834