4.13.48 $$x (a+y(x))^2 y'(x)=b y(x)^2$$

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 = 0.417532 (sec), leaf count = 32

$\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {a^2}{\text {\#1}}+2 a \log (\text {\#1})+\text {\#1}\& \right ][b \log (x)+c_1]\right \}\right \}$

Maple
cpu = 0.31 (sec), leaf count = 33

$[y \left (x \right ) = {\mathrm e}^{\RootOf \left (\ln \left (x \right ) b \,{\mathrm e}^{\textit {\_Z}}+\textit {\_C1} b \,{\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}}+a^{2}\right )}]$ 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))

Maple raw output

[y(x) = exp(RootOf(ln(x)*b*exp(_Z)+_C1*b*exp(_Z)-2*_Z*a*exp(_Z)-exp(2*_Z)+a^2))]