ODE
\[ y'(x)^3+\left (e^{2 x}+e^{3 x}\right ) e^{-2 y(x)} y'(x)-e^{3 x-2 y(x)}=0 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of variable
Mathematica ✗
cpu = 600.083 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 2.609 (sec), leaf count = 26
\[\left [y \left (x \right ) = x -\frac {\ln \left (-\frac {1}{\left ({\mathrm e}^{-x} \textit {\_C1} -1\right )^{2} \left (\textit {\_C1} +1\right )}\right )}{2}\right ]\] Mathematica raw input
DSolve[-E^(3*x - 2*y[x]) + ((E^(2*x) + E^(3*x))*y'[x])/E^(2*y[x]) + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3+exp(-2*y(x))*(exp(2*x)+exp(3*x))*diff(y(x),x)-exp(3*x-2*y(x)) = 0, y(x))
Maple raw output
[y(x) = x-1/2*ln(-1/(1/exp(x)*_C1-1)^2/(_C1+1))]