ODE
\[ (a+y(x)) y''(x)=y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.309483 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -a+e^{c_1 (x+c_2)}\right \}\right \}\]
Maple ✓
cpu = 1.299 (sec), leaf count = 14
\[[y \left (x \right ) = {\mathrm e}^{\textit {\_C1} x} \textit {\_C2} -a]\] Mathematica raw input
DSolve[(a + y[x])*y''[x] == y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -a + E^(C[1]*(x + C[2]))}}
Maple raw input
dsolve((a+y(x))*diff(diff(y(x),x),x) = diff(y(x),x)^2, y(x))
Maple raw output
[y(x) = exp(_C1*x)*_C2-a]