ODE
\[ y(x) y''(x)+y'(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.289383 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 \sqrt {2 x-c_1}\right \}\right \}\]
Maple ✓
cpu = 0.09 (sec), leaf count = 29
\[\left [y \left (x \right ) = \sqrt {2 \textit {\_C1} x +2 \textit {\_C2}}, y \left (x \right ) = -\sqrt {2 \textit {\_C1} x +2 \textit {\_C2}}\right ]\] Mathematica raw input
DSolve[y'[x]^2 + y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[2*x - C[1]]*C[2]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+diff(y(x),x)^2 = 0, y(x))
Maple raw output
[y(x) = (2*_C1*x+2*_C2)^(1/2), y(x) = -(2*_C1*x+2*_C2)^(1/2)]