2.3.217 Problems 21601 to 21700

Table 2.965: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21601	15385	\begin{align*} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	4.681
21602	8310	\begin{align*} y^{\prime } y&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.682
21603	11800	\begin{align*} {y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d&=0 \\ \end{align*}	✓	✓	✓	✓	4.683
21604	5589	\begin{align*} \left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.685
21605	23122	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.686
21606	19985	\begin{align*} y&=y {y^{\prime }}^{2}+2 y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	4.687
21607	18054	\begin{align*} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.688
21608	10110	\begin{align*} y^{\prime \prime }-y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.690
21609	21254	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ \end{align*}	✓	✓	✓	✗	4.690
21610	5119	\begin{align*} \left (a x +b y\right ) y^{\prime }+b x +a y&=0 \\ \end{align*}	✓	✓	✓	✓	4.691
21611	11639	\begin{align*} x \left (y \ln \left (y x \right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (y x \right )-y+a x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.693
21612	12697	\begin{align*} y^{\prime \prime }&=-\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	4.696
21613	13974	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.696
21614	19252	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.697
21615	4356	\begin{align*} y^{2} x^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.698
21616	5185	\begin{align*} x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \\ \end{align*}	✓	✓	✓	✓	4.698
21617	2998	\begin{align*} y+y^{\prime }&=y^{2} {\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.699
21618	6264	\begin{align*} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.702
21619	4304	\begin{align*} y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.703
21620	4826	\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	4.703
21621	23198	\begin{align*} y-\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.704
21622	19902	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.706
21623	19789	\begin{align*} y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	4.709
21624	25757	\begin{align*} y^{\prime } x +y&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.709
21625	2991	\begin{align*} y^{\prime } x +y&=y^{2} x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.710
21626	5146	\begin{align*} x \left (x +y\right ) y^{\prime }&=y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✗	4.710
21627	19319	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.712
21628	25760	\begin{align*} \left (y x +1\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.713
21629	4863	\begin{align*} 3 y^{\prime } x&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.720
21630	4983	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.720
21631	21056	\begin{align*} x^{\prime }&={\mathrm e}^{t} \left (1+x^{2}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.720
21632	6903	\begin{align*} 2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 \,{\mathrm e}^{\frac {x}{y}} x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.725
21633	9082	\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}	✓	✓	✓	✓	4.726
21634	15358	\begin{align*} x +2 y+1-\left (3+2 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.727
21635	15621	\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.727
21636	21337	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.728
21637	22500	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	4.728
21638	13960	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.731
21639	4440	\begin{align*} x +\sin \left (\frac {y}{x}\right )^{2} \left (y-y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.733
21640	12855	\begin{align*} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \\ \end{align*}	✗	✗	✗	✗	4.734
21641	14014	\begin{align*} y^{\prime } x -a y+b y^{2}&=c \,x^{2 a} \\ \end{align*}	✓	✓	✓	✗	4.734
21642	7681	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	4.736
21643	13977	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.737
21644	8885	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.741
21645	19390	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	4.741
21646	21098	\begin{align*} x&=t x^{\prime }-{\mathrm e}^{x^{\prime }} \\ \end{align*}	✓	✓	✓	✓	4.741
21647	14447	\begin{align*} \frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.742
21648	5845	\begin{align*} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.743
21649	5088	\begin{align*} \left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.744
21650	7509	\begin{align*} y^{\prime }+\frac {y}{x}&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	4.744
21651	11424	\begin{align*} y^{\prime } x +\tan \left (\frac {y}{x}\right ) x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.745
21652	2516	\begin{align*} 2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.746
21653	3295	\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	4.746
21654	17880	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.747
21655	4821	\begin{align*} y^{\prime } x&=y+x \sin \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.749
21656	6857	\begin{align*} -y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.750
21657	17927	\begin{align*} 4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.750
21658	13235	\begin{align*} y^{\prime }&=-a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \\ \end{align*}	✓	✓	✓	✗	4.751
21659	22430	\begin{align*} x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.753
21660	5331	\begin{align*} x \left (a +x y^{n}\right ) y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	4.756
21661	14467	\begin{align*} \tan \left (\frac {y}{x}\right ) x +y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.757
21662	4697	\begin{align*} y^{\prime }&=\left (a +b x y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.759
21663	13348	\begin{align*} y^{\prime } x&=a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2} \\ \end{align*}	✓	✓	✓	✗	4.759
21664	5300	\begin{align*} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	4.761
21665	8213	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	4.761
21666	1598	\begin{align*} y^{\prime }+x^{2} \left (1+y\right ) \left (y-2\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.762
21667	19070	\begin{align*} y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\ \end{align*}	✓	✓	✓	✓	4.763
21668	22408	\begin{align*} y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x +1\right )} \\ \end{align*}	✓	✓	✓	✓	4.763
21669	20689	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	4.764
21670	5702	\begin{align*} \ln \left (y^{\prime }\right )+y^{\prime } x +a +b y&=0 \\ \end{align*}	✓	✓	✓	✓	4.766
21671	11855	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	4.771
21672	2938	\begin{align*} \left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.773
21673	1662	\begin{align*} x^{2} y^{\prime }&=y^{2}+y x -4 x^{2} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.775
21674	5125	\begin{align*} x y^{\prime } y+x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.776
21675	9017	\begin{align*} y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \\ \end{align*}	✓	✓	✓	✓	4.777
21676	5101	\begin{align*} \left (x +4 y\right ) y^{\prime }+4 x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.782
21677	11457	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.782
21678	14000	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.783
21679	25723	\begin{align*} y^{\prime } y&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	4.790
21680	4801	\begin{align*} y^{\prime } x&=a y+b \left (-x^{2}+1\right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	4.793
21681	20277	\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.793
21682	20680	\begin{align*} \left (x +2 y^{3}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	4.795
21683	12701	\begin{align*} y^{\prime \prime }&=-\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	4.796
21684	16351	\begin{align*} \sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.796
21685	17100	\begin{align*} y^{\prime }&=\sin \left (t -y\right )+\sin \left (t +y\right ) \\ \end{align*}	✓	✓	✓	✓	4.799
21686	22554	\begin{align*} -y+y^{\prime } x&=x^{2} y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.799
21687	23837	\begin{align*} y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	4.799
21688	12071	\begin{align*} y^{\prime }&=-\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )} \\ \end{align*}	✓	✗	✓	✗	4.800
21689	17913	\begin{align*} x^{2} y^{\prime }&=x^{2}-y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	4.802
21690	11615	\begin{align*} \left (2 x^{2} y^{3}+y^{2} x^{2}-2 x \right ) y^{\prime }-2 y-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.804
21691	14198	\begin{align*} 2 t x^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	4.804
21692	21105	\begin{align*} x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.804
21693	15551	\begin{align*} y^{\prime }&=\frac {y}{y-x} \\ \end{align*}	✓	✓	✓	✓	4.807
21694	4352	\begin{align*} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.810
21695	8660	\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.812
21696	186	\begin{align*} x^{2} y^{\prime }+2 y x&=y^{2} \\ \end{align*}	✓	✓	✓	✓	4.813
21697	6816	\begin{align*} y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \\ \end{align*}	✓	✓	✓	✓	4.813
21698	5173	\begin{align*} x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.819
21699	14471	\begin{align*} y+2+y \left (x +4\right ) y^{\prime }&=0 \\ y \left (-3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.819
21700	19357	\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	4.820