ODE
\[ y''(x)=e^x y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.331401 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {-x+\log \left (e^x+c_1\right )+c_1 c_2}{c_1}\right \}\right \}\]
Maple ✓
cpu = 0.415 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\ln \left ({\mathrm e}^{x}\right )}{\textit {\_C1}}-\frac {\ln \left ({\mathrm e}^{x}-\textit {\_C1} \right )}{\textit {\_C1}}+\textit {\_C2}\right ]\] 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))
Maple raw output
[y(x) = 1/_C1*ln(exp(x))-1/_C1*ln(exp(x)-_C1)+_C2]