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 = 0.0338641 (sec), leaf count = 18
\[\left \{\left \{y(x)\to e^{c_1 \left (c_2+x\right )}-a\right \}\right \}\]
Maple ✓
cpu = 0.028 (sec), leaf count = 16
\[ \left \{ \ln \left ( a+y \left ( x \right ) \right ) -{\it \_C1}\,x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
ln(a+y(x))-_C1*x-_C2 = 0