ODE
\[ y(x) y''(x)=-x^2 y(x)^2+y'(x)^2+y(x)^2 \log (y(x)) \] ODE Classification
[[_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.168172 (sec), leaf count = 30
\[\left \{\left \{y(x)\to e^{-\frac {c_1 e^x}{2}-c_2 e^{-x}+x^2+2}\right \}\right \}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 30
\[ \left \{ -{{\rm e}^{2\,x}}{\it \_C1}+2\,{x}^{2}{{\rm e}^{x}}-2\,{{\rm e}^{x}}\ln \left ( y \left ( x \right ) \right ) +4\,{{\rm e}^{x}}+{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == -(x^2*y[x]^2) + Log[y[x]]*y[x]^2 + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> E^(2 + x^2 - (E^x*C[1])/2 - C[2]/E^x)}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+y(x)^2*ln(y(x))-x^2*y(x)^2, y(x),'implicit')
Maple raw output
-exp(2*x)*_C1+2*x^2*exp(x)-2*exp(x)*ln(y(x))+4*exp(x)+_C2 = 0