2.3.217 Problems 21601 to 21700

Table 2.1007: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21601	7332	\begin{align*} x^{2} y^{\prime }-y x&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	4.954
21602	5820	\begin{align*} -a y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.956
21603	6589	\begin{align*} 4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	4.957
21604	11697	\begin{align*} x {y^{\prime }}^{2}+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.958
21605	4348	\begin{align*} y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.960
21606	5000	\begin{align*} \left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\ \end{align*}	✓	✓	✓	✗	4.961
21607	25497	\begin{align*} y^{\prime }&=\frac {y^{2}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	4.963
21608	7387	\begin{align*} x^{\prime }&=3 t^{2} x \\ \end{align*}	✓	✓	✓	✓	4.964
21609	8372	\begin{align*} y^{\prime }&=\frac {1+3 x}{2 y} \\ y \left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.964
21610	11804	\begin{align*} {y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.964
21611	26089	\begin{align*} x y^{2}+x^{2} y y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	4.965
21612	2883	\begin{align*} y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.967
21613	19286	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.967
21614	19673	\begin{align*} x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\ \end{align*}	✓	✓	✓	✓	4.968
21615	3450	\begin{align*} y^{\prime }&=\frac {2 y}{1+t} \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	4.969
21616	201	\begin{align*} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.970
21617	21926	\begin{align*} x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.970
21618	3320	\begin{align*} 3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\ \end{align*}	✓	✓	✗	✗	4.972
21619	9161	\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	4.972
21620	6963	\begin{align*} y^{\prime } x +y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	4.976
21621	7861	\begin{align*} y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (y-y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.977
21622	5158	\begin{align*} 2 y y^{\prime } x +a +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.981
21623	17074	\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}	✓	✓	✓	✓	4.981
21624	17118	\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.982
21625	25851	\begin{align*} y+3 x +y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.983
21626	12578	\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.985
21627	17015	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.986
21628	5555	\begin{align*} \left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.987
21629	4898	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.988
21630	23910	\begin{align*} y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\ \end{align*}	✓	✓	✓	✓	4.989
21631	23849	\begin{align*} 2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.990
21632	4260	\begin{align*} \left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	4.992
21633	7528	\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\ \end{align*}	✓	✓	✓	✓	4.993
21634	14221	\begin{align*} \left (2 u+1\right ) u^{\prime }-1-t&=0 \\ \end{align*}	✓	✓	✓	✓	4.993
21635	802	\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	4.994
21636	26248	\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\ y \left (\infty \right ) &= 2 \pi \\ \end{align*}	✓	✓	✗	✗	4.994
21637	27389	\begin{align*} x^{2} {y^{\prime }}^{2}&=y y^{\prime } x +1 \\ \end{align*}	✓	✓	✓	✓	4.994
21638	2970	\begin{align*} \cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.995
21639	4899	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.999
21640	19711	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.000
21641	26090	\begin{align*} 2 x -1-\frac {y}{x^{2}}-\left (2 y-\frac {1}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.000
21642	6357	\begin{align*} y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	5.001
21643	13288	\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2} \\ \end{align*}	✓	✓	✓	✗	5.002
21644	22774	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\left (3 \sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.003
21645	13204	\begin{align*} g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{0} \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.004
21646	11839	\begin{align*} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.006
21647	12420	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.006
21648	26672	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y&=4 \,{\mathrm e}^{x} \\ y \left (-\infty \right ) &= 0 \\ y^{\prime }\left (-1\right ) &= -{\mathrm e}^{-1} \\ \end{align*}	✓	✓	✓	✗	5.006
21649	2982	\begin{align*} y^{3} y^{\prime }+y^{4} x&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.007
21650	21846	\begin{align*} y^{\prime } x +y&=y^{2} x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.008
21651	26463	\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	5.008
21652	24032	\begin{align*} y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\ \end{align*}	✓	✓	✓	✗	5.009
21653	17082	\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}	✓	✓	✓	✓	5.010
21654	7002	\begin{align*} y^{\prime }&=\left (x^{2}+2 y-1\right )^{{2}/{3}}-x \\ \end{align*}	✓	✓	✓	✓	5.012
21655	5183	\begin{align*} x \left (y x +2\right ) y^{\prime }&=3+2 x^{3}-2 y-x y^{2} \\ \end{align*}	✓	✓	✓	✗	5.013
21656	17910	\begin{align*} y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	5.013
21657	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*}	✓	✓	✓	✓	5.013
21658	24077	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.016
21659	19792	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=x^{3}-x^{2} \arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.017
21660	7354	\begin{align*} \sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2}&=r \cos \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.018
21661	13953	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.018
21662	21795	\begin{align*} y^{\prime }&=-\frac {x}{4 y} \\ \end{align*}	✓	✓	✓	✓	5.020
21663	21965	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.020
21664	24301	\begin{align*} y \left (y \,{\mathrm e}^{y x}+1\right )+\left (x y \,{\mathrm e}^{y x}+{\mathrm e}^{y x}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.020
21665	8316	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	5.022
21666	12010	\begin{align*} y^{\prime }&=\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.022
21667	14017	\begin{align*} y^{\prime }-x^{2} y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	5.023
21668	11621	\begin{align*} \left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.029
21669	20350	\begin{align*} a^{2} y+y^{\prime \prime }&=\cos \left (a x \right )+\cos \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	5.032
21670	11615	\begin{align*} \left (2 x^{2} y^{3}+y^{2} x^{2}-2 x \right ) y^{\prime }-2 y-1&=0 \\ \end{align*}	✓	✓	✓	✓	5.034
21671	26220	\begin{align*} \left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.034
21672	20218	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.036
21673	7184	\begin{align*} \left (-x^{2}+x \right ) y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.037
21674	19895	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.039
21675	13996	\begin{align*} y^{\prime }-\frac {1+y}{x +1}&=\sqrt {1+y} \\ \end{align*}	✓	✓	✓	✓	5.040
21676	13414	\begin{align*} y^{\prime }&=y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	5.042
21677	4993	\begin{align*} x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.046
21678	17083	\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}	✓	✓	✓	✓	5.047
21679	17800	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	5.047
21680	19316	\begin{align*} y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.048
21681	5505	\begin{align*} x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.052
21682	5019	\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=\sqrt {y^{3}+1} \\ \end{align*}	✓	✓	✓	✓	5.053
21683	6345	\begin{align*} h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.053
21684	19676	\begin{align*} 2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✗	5.054
21685	3014	\begin{align*} y-y^{\prime } x&=2 y^{\prime }+2 y^{2} \\ \end{align*}	✓	✓	✓	✓	5.056
21686	4432	\begin{align*} 2 y^{\prime }+x&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✗	5.056
21687	8290	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (3\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.058
21688	11348	\begin{align*} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\ \end{align*}	✓	✓	✓	✗	5.058
21689	19274	\begin{align*} v^{\prime }&=g -\frac {k v^{2}}{m} \\ \end{align*}	✓	✓	✓	✓	5.059
21690	2501	\begin{align*} y^{\prime } t&=y+\sqrt {t^{2}+y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.063
21691	6269	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.063
21692	16342	\begin{align*} 3 y-x^{3}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.065
21693	5351	\begin{align*} \left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.066
21694	3467	\begin{align*} y^{\prime }&=\frac {1}{x +2 y+1} \\ \end{align*}	✓	✓	✓	✓	5.067
21695	23858	\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.068
21696	5578	\begin{align*} y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.069
21697	4240	\begin{align*} x^{2}-y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.072
21698	27481	\begin{align*} y&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	5.075
21699	1349	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.076
21700	4092	\begin{align*} 3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.079