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	2532	\begin{align*} y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\ y \left (0\right ) &= 100 \\ \end{align*}	✓	✓	✓	✓	5.923
21602	11628	\begin{align*} \sqrt {y^{2}-1}\, y^{\prime }-\sqrt {x^{2}-1}&=0 \\ \end{align*}	✓	✓	✓	✓	5.924
21603	8212	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.925
21604	12380	\begin{align*} x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✗	✓	✓	✗	5.926
21605	14290	\begin{align*} x^{\prime \prime }-12 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.926
21606	20587	\begin{align*} x^{4} y^{\prime \prime }-x^{3} y^{\prime }&={y^{\prime }}^{2} x^{2}-4 y^{2} \\ \end{align*}	✗	✓	✓	✗	5.927
21607	22379	\begin{align*} y^{\prime }&=1+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.932
21608	25707	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.934
21609	11332	\begin{align*} y^{\prime }+x^{-a -1} y^{2}-x^{a}&=0 \\ \end{align*}	✓	✓	✓	✗	5.936
21610	5559	\begin{align*} \left (1-a y\right ) {y^{\prime }}^{2}&=a y \\ \end{align*}	✓	✓	✓	✓	5.937
21611	8775	\begin{align*} \left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y&=\left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	5.938
21612	18582	\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.940
21613	11868	\begin{align*} y^{\prime }&=F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \\ \end{align*}	✗	✓	✓	✗	5.941
21614	18100	\begin{align*} y^{\prime \prime \prime }&=\sqrt {1-{y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✗	✓	✓	5.945
21615	11962	\begin{align*} y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 x^{2} y^{2}+7 x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	5.947
21616	8838	\begin{align*} x y^{\prime }-y&=x \sqrt {x^{2}-y^{2}}\, y^{\prime } \\ \end{align*}	✓	✓	✓	✗	5.948
21617	22997	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=x \\ \end{align*}	✓	✓	✓	✓	5.948
21618	25823	\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right ) x^{2}}{\left (y+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	5.948
21619	12016	\begin{align*} y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{3}\right ) y}{x +1} \\ \end{align*}	✗	✓	✓	✓	5.949
21620	17328	\begin{align*} t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.949
21621	12178	\begin{align*} y^{\prime }&=\frac {32 x^{5} y+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	5.950
21622	2986	\begin{align*} y^{\prime }-y x&=\sqrt {y}\, x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.951
21623	11483	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\ \end{align*}	✓	✓	✓	✗	5.952
21624	8346	\begin{align*} y \ln \left (x \right ) y^{\prime }&=\frac {\left (y+1\right )^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.953
21625	5002	\begin{align*} x \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	5.954
21626	15841	\begin{align*} y^{\prime }&=\sin \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.954
21627	18491	\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.955
21628	22471	\begin{align*} y-x^{5} y^{4}+\left (x -x^{4} y^{5}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.955
21629	5765	\begin{align*} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.958
21630	18162	\begin{align*} y^{\prime \prime }+k^{2} y&=k \\ \end{align*}	✓	✓	✓	✓	5.959
21631	17059	\begin{align*} y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.964
21632	11423	\begin{align*} x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.966
21633	21565	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	5.967
21634	24128	\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.968
21635	9788	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.970
21636	22550	\begin{align*} n^{\prime }&=-a n \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	5.971
21637	6508	\begin{align*} a y y^{\prime }+2 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.972
21638	7478	\begin{align*} 2 x y^{2}-y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.973
21639	21029	\begin{align*} x^{\prime }&=\frac {3 x^{{1}/{3}}}{2} \\ x \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✗	5.973
21640	4823	\begin{align*} x y^{\prime }+x +\tan \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.974
21641	14243	\begin{align*} \cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.976
21642	24313	\begin{align*} y^{2}+y-\left (y^{2}+2 y x +x \right ) y^{\prime }&=0 \\ y \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.976
21643	1733	\begin{align*} 3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.977
21644	4722	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.980
21645	1731	\begin{align*} y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.984
21646	26226	\begin{align*} 1+y^{2}&=\left (y-\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.992
21647	15587	\begin{align*} y^{\prime }&=y x +x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.993
21648	15407	\begin{align*} y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.994
21649	18489	\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \\ y \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	5.995
21650	12242	\begin{align*} y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-y^{6} a^{2}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\ \end{align*}	✓	✓	✓	✗	5.996
21651	25898	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.997
21652	17089	\begin{align*} \tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.998
21653	14253	\begin{align*} \left (t^{2}+1\right ) x^{\prime }&=-3 x t +6 t \\ \end{align*}	✓	✓	✓	✓	6.000
21654	11875	\begin{align*} y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \\ \end{align*}	✗	✓	✓	✗	6.003
21655	5883	\begin{align*} 4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\ \end{align*}	✗	✓	✓	✗	6.004
21656	9769	\begin{align*} 2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	6.004
21657	15965	\begin{align*} y^{\prime }&=\left (-2+y\right ) \left (y+1-\cos \left (t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	6.006
21658	11941	\begin{align*} y^{\prime }&=-\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✓	6.011
21659	12231	\begin{align*} y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} y^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 a \,x^{3} y}{4}+\frac {3 a^{2} x^{2} y}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \\ \end{align*}	✓	✓	✓	✗	6.011
21660	21683	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.013
21661	7448	\begin{align*} \sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.014
21662	15603	\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	6.018
21663	24269	\begin{align*} x y^{\prime }+x +y&=0 \\ \end{align*}	✓	✓	✓	✓	6.018
21664	17097	\begin{align*} y^{\prime }&=y^{2} t^{2}+y^{2}-t^{2}-1 \\ \end{align*}	✓	✓	✓	✗	6.022
21665	25466	\begin{align*} y^{\prime }&=\sin \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.022
21666	25000	\begin{align*} t y^{\prime }+3 y&=t^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	6.023
21667	4705	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\ \end{align*}	✗	✗	✗	✗	6.024
21668	15372	\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\ \end{align*}	✓	✓	✓	✓	6.025
21669	17939	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.025
21670	3412	\begin{align*} x y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	6.028
21671	4847	\begin{align*} \left (x +a \right ) y^{\prime }&=b x +c y \\ \end{align*}	✓	✓	✓	✓	6.030
21672	25827	\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left (1+{\mathrm e}^{x}\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.030
21673	8799	\begin{align*} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.031
21674	27214	\begin{align*} \sqrt {1+y^{2}}&=x y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	6.031
21675	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*}	✓	✓	✓	✗	6.032
21676	15120	\begin{align*} x y^{\prime }+y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	6.033
21677	17717	\begin{align*} y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.035
21678	769	\begin{align*} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	6.036
21679	18353	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.038
21680	13781	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	6.039
21681	6177	\begin{align*} -9 y-3 \left (-3 x +1\right ) y^{\prime }+\left (-3 x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.044
21682	22070	\begin{align*} y^{\prime }+6 y x&=0 \\ y \left (\pi \right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	6.045
21683	11920	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1} \\ \end{align*}	✓	✓	✓	✗	6.046
21684	18769	\begin{align*} 4 y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.046
21685	106	\begin{align*} 2 x y y^{\prime }&=x^{2}+2 y^{2} \\ \end{align*}	✓	✓	✓	✓	6.049
21686	13400	\begin{align*} y^{\prime }&=y^{2}+\lambda a +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✗	✗	6.049
21687	24329	\begin{align*} x y^{\prime }&=y-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.049
21688	25351	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	6.049
21689	13974	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.050
21690	5990	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.052
21691	22968	\begin{align*} \frac {y}{x}+\ln \left (x \right ) y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	6.052
21692	23245	\begin{align*} \sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=1 \\ \end{align*}	✓	✓	✓	✗	6.052
21693	4913	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	6.053
21694	16335	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	6.053
21695	26239	\begin{align*} y^{\prime }&=y^{a} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	6.056
21696	25793	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	6.059
21697	25857	\begin{align*} x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.060
21698	17076	\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	6.062
21699	20270	\begin{align*} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=\sin \left (x \right )+y \\ \end{align*}	✓	✓	✓	✗	6.062
21700	4753	\begin{align*} x y^{\prime }&=x^{3}-y \\ \end{align*}	✓	✓	✓	✓	6.066