2.1667   ODE No. 1667

\[ b x^{5-2 a} e^{y(x)}+a y'(x)+x y''(x)=0 \] Mathematica : cpu = 0.389223 (sec), leaf count = 0

DSolve[b*E^y[x]*x^(5 - 2*a) + a*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
 

, could not solve

DSolve[b*E^y[x]*x^(5 - 2*a) + a*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0. (sec), leaf count = 0

dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x^(5-2*a)*exp(y(x))=0,y(x))
 

, result contains DESol or ODESolStruc

\[y \left (x \right ) = \left (\textit {\_a} +2 a \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right )-6 \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right )-6 c_{1}\right )\:\& \text {where}\:\left [\left \{\frac {d}{d \textit {\_a}}\textit {\_}b\left (\textit {\_a} \right )=\left (b \,{\mathrm e}^{\textit {\_a}}+2 a^{2}-8 a +6\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\left (a -1\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \left (x \right )-\left (2 a -6\right ) \ln \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \left (x \right )\right )-2 a +6}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \left (x \right )=\textit {\_a} +2 a \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right )-6 \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right )-6 c_{1}\right \}\right ]\]