4.39.8 \(y(x) y''(x)=y'(x)^2-y'(x)\)

ODE
\[ y(x) y''(x)=y'(x)^2-y'(x) \] ODE Classification

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica
cpu = 0.0271559 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {e^{c_1 \left (c_2+x\right )}-1}{c_1}\right \}\right \}\]

Maple
cpu = 0.051 (sec), leaf count = 21

\[ \left \{ {\frac {\ln \left ( {\it \_C1}\,y \left ( x \right ) +1 \right ) }{{\it \_C1}}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input

DSolve[y[x]*y''[x] == -y'[x] + y'[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> (-1 + E^(C[1]*(x + C[2])))/C[1]}}

Maple raw input

dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-diff(y(x),x), y(x),'implicit')

Maple raw output

ln(_C1*y(x)+1)/_C1-x-_C2 = 0