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 = 0.0253791 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 \sqrt {2 x-c_1}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 17
\[ \left \{ {\frac { \left ( y \left ( x \right ) \right ) ^{2}}{2}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
1/2*y(x)^2-_C1*x-_C2 = 0