ODE
\[ x^2 y''(x)+y'(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0150918 (sec), leaf count = 27
\[\left \{\left \{y(x)\to -\frac {x}{c_1}+\frac {\log \left (c_1 x+1\right )}{c_1^2}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.3 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\frac {x}{{\it \_C1}}}+{\frac {\ln \left ( {\it \_C1}\,x-1 \right ) }{{{\it \_C1}}^{2}}}+{\it \_C2} \right \} \] Mathematica raw input
DSolve[y'[x]^2 + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x/C[1]) + C[2] + Log[1 + x*C[1]]/C[1]^2}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+diff(y(x),x)^2 = 0, y(x),'implicit')
Maple raw output
y(x) = 1/_C1*x+1/_C1^2*ln(_C1*x-1)+_C2