ODE
\[ x (a+y(x))^2 y'(x)=b y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0569887 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {a^2}{\text {$\#$1}}+2 a \log (\text {$\#$1})+\text {$\#$1}\& \right ]\left [b \log (x)+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 34
\[ \left \{ \ln \left ( x \right ) -{\frac {y \left ( x \right ) }{b}}+{\frac {{a}^{2}}{by \left ( x \right ) }}-2\,{\frac {a\ln \left ( y \left ( x \right ) \right ) }{b}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*(a + y[x])^2*y'[x] == b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[2*a*Log[#1] - a^2/#1 + #1 & ][C[1] + b*Log[x]]}}
Maple raw input
dsolve(x*(a+y(x))^2*diff(y(x),x) = b*y(x)^2, y(x),'implicit')
Maple raw output
ln(x)-1/b*y(x)+1/b*a^2/y(x)-2/b*a*ln(y(x))+_C1 = 0