2.3.188 Problems 18701 to 18800

Table 2.907: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18701	24186	\begin{align*} y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.912
18702	8972	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.913
18703	21608	\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	5.913
18704	1831	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=2 \left (x -1\right )^{2} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	5.915
18705	14288	\begin{align*} x^{\prime \prime }-4 x^{\prime }+6 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.915
18706	16600	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=22 x +24 \\ \end{align*}	✓	✓	✓	✓	5.916
18707	6983	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.918
18708	3600	\begin{align*} y^{\prime }&=\frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}	✓	✓	✓	✓	5.919
18709	20556	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=a x \\ \end{align*}	✓	✓	✓	✓	5.919
18710	13940	\begin{align*} y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.921
18711	4970	\begin{align*} x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.924
18712	21485	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.925
18713	12190	\begin{align*} y^{\prime }&=\frac {-2 x -y+1+y^{2} x^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x} \\ \end{align*}	✓	✓	✓	✗	5.927
18714	12440	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{5} \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.927
18715	20495	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	5.927
18716	21791	\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.927
18717	8752	\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.930
18718	18249	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.931
18719	24648	\begin{align*} y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	5.931
18720	6921	\begin{align*} y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.932
18721	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*}	✗	✓	✓	✗	5.935
18722	19281	\begin{align*} y^{\prime } x&=2 x +3 y \\ \end{align*}	✓	✓	✓	✓	5.935
18723	18772	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.936
18724	5369	\begin{align*} {y^{\prime }}^{2}&=a^{2} y^{n} \\ \end{align*}	✓	✓	✓	✓	5.938
18725	17067	\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.944
18726	20285	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.944
18727	8982	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y&=x \\ \end{align*}	✓	✓	✓	✓	5.945
18728	12305	\begin{align*} y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.949
18729	19474	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.953
18730	14287	\begin{align*} x^{\prime \prime }+x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.955
18731	4320	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\ \end{align*}	✓	✓	✓	✓	5.956
18732	18345	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.957
18733	10159	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.960
18734	3009	\begin{align*} 2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.961
18735	4318	\begin{align*} \left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	5.961
18736	22971	\begin{align*} y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✓	5.961
18737	9387	\begin{align*} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.965
18738	4883	\begin{align*} x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	5.967
18739	8377	\begin{align*} y^{\prime }&=y^{2}-4 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	5.967
18740	2559	\begin{align*} y^{\prime \prime }+y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.968
18741	3524	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\ \end{align*}	✓	✓	✓	✓	5.968
18742	20272	\begin{align*} y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.968
18743	13336	\begin{align*} y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	5.969
18744	15501	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.969
18745	16514	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.969
18746	17513	\begin{align*} y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	5.969
18747	9736	\begin{align*} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.970
18748	11563	\begin{align*} f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.970
18749	736	\begin{align*} x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✗	5.971
18750	5118	\begin{align*} \left (a x +b y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.972
18751	19078	\begin{align*} y^{\prime } x -4 y&=\sqrt {y}\, x^{2} \\ \end{align*}	✓	✓	✓	✓	5.972
18752	9531	\begin{align*} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.974
18753	23222	\begin{align*} y^{\prime }&=-\frac {x +2 y}{y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.974
18754	6904	\begin{align*} {\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.976
18755	7064	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.976
18756	8380	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.977
18757	8980	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.977
18758	1827	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=x^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	5.978
18759	6989	\begin{align*} y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.978
18760	21759	\begin{align*} y^{\prime \prime } x -{y^{\prime }}^{3}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.979
18761	7561	\begin{align*} \sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	5.980
18762	15255	\begin{align*} t^{2} y^{\prime \prime }-6 y^{\prime } t +\sin \left (2 t \right ) y&=\ln \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	5.986
18763	17918	\begin{align*} x +y-2+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.987
18764	25721	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.987
18765	8235	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.988
18766	3229	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.990
18767	13910	\begin{align*} \left (a \,x^{n}+b x +c \right ) y^{\prime \prime }&=a n \left (n -1\right ) x^{-2+n} y \\ \end{align*}	✓	✓	✗	✗	5.990
18768	20682	\begin{align*} 1+y^{2}-y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.990
18769	22458	\begin{align*} y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.991
18770	5093	\begin{align*} \left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\ \end{align*}	✓	✓	✓	✗	5.992
18771	5901	\begin{align*} y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	5.992
18772	107	\begin{align*} y^{\prime } x&=y+2 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	5.995
18773	11311	\begin{align*} y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.995
18774	16509	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.995
18775	4987	\begin{align*} x^{2} \left (1-x \right ) y^{\prime }&=x \left (-x +2\right ) y-y^{2} \\ \end{align*}	✓	✓	✓	✓	5.996
18776	18727	\begin{align*} y^{\prime \prime }+y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.997
18777	22484	\begin{align*} y^{\prime } y^{\prime \prime }&=1 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.997
18778	17780	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.998
18779	4401	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\ \end{align*}	✓	✓	✓	✗	5.999
18780	10454	\begin{align*} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	5.999
18781	5221	\begin{align*} \left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✗	6.000
18782	4962	\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\ \end{align*}	✓	✓	✓	✓	6.001
18783	6918	\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.002
18784	23198	\begin{align*} y-\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.002
18785	7869	\begin{align*} y y^{\prime } x&=\left (1+y\right ) \left (1-x \right ) \\ \end{align*}	✓	✓	✓	✓	6.003
18786	20334	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.003
18787	15417	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.004
18788	11974	\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x} \\ \end{align*}	✓	✓	✓	✗	6.005
18789	10318	\begin{align*} y^{\prime }&=\sqrt {1+6 x +y} \\ \end{align*}	✓	✓	✓	✓	6.006
18790	12182	\begin{align*} y^{\prime }&=\frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}}{\left (-y^{2}+x^{2}-1\right ) y} \\ \end{align*}	✓	✓	✓	✗	6.007
18791	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*}	✗	✓	✗	✗	6.008
18792	17511	\begin{align*} y^{\prime \prime }+y&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	6.010
18793	9651	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	6.013
18794	9162	\begin{align*} y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	6.016
18795	3602	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\ \end{align*}	✓	✓	✓	✓	6.017
18796	6160	\begin{align*} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.018
18797	21021	\begin{align*} x^{\prime }+x&=4 t \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.018
18798	12035	\begin{align*} y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✓	6.020
18799	21874	\begin{align*} y^{\prime \prime }-12 y^{\prime }+35 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.020
18800	13454	\begin{align*} y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right ) \\ \end{align*}	✓	✓	✗	✗	6.023