4.37.13 \(y''(x)=e^x y'(x)^2\)

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