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 = 600.047 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.994 (sec), leaf count = 42
\[ \left \{ [y \left ( {\it \_T} \right ) =-\ln \left ( {\it \_T}-1 \right ) +\ln \left ( {\it \_T} \right ) +{\it \_C1}-{\frac {1}{2}\ln \left ( -{\frac {{{\it \_T}}^{2}}{{{\rm e}^{{\it \_C1}}}+1}} \right ) },x \left ( {\it \_T} \right ) =-\ln \left ( {\it \_T}-1 \right ) +\ln \left ( {\it \_T} \right ) +{\it \_C1}] \right \} \] 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),'implicit')
Maple raw output
[y(_T) = -ln(_T-1)+ln(_T)+_C1-1/2*ln(-_T^2/(exp(_C1)+1)), x(_T) = -ln(_T-1)+ln(_T)+_C1]