ODE
\[ y''(x)=e^x y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0150912 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {\log \left (c_1+e^x\right )+c_1 c_2-x}{c_1}\right \}\right \}\]
Maple ✓
cpu = 0.098 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,{\it \_C1}-\ln \left ( {{\rm e}^{x}}-{\it \_C1} \right ) +\ln \left ( {{\rm e}^{x}} \right ) }{{\it \_C1}}} \right \} \] Mathematica raw input
DSolve[y''[x] == E^x*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-x + C[1]*C[2] + Log[E^x + C[1]])/C[1]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = exp(x)*diff(y(x),x)^2, y(x),'implicit')
Maple raw output
y(x) = (_C2*_C1-ln(exp(x)-_C1)+ln(exp(x)))/_C1