ODE
\[ x^2 y'(x)=y(x) (a x+b y(x)) \] ODE Classification
[[_homogeneous, `class A`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.254605 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\frac {(a-1) x^{a+1}}{b x^a-(a-1) c_1 x}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 33
\[\left [y \left (x \right ) = \frac {x \left (a -1\right )}{x^{-a} \textit {\_C1} x a -x^{-a} \textit {\_C1} x -b}\right ]\] Mathematica raw input
DSolve[x^2*y'[x] == y[x]*(a*x + b*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> -(((-1 + a)*x^(1 + a))/(b*x^a - (-1 + a)*x*C[1]))}}
Maple raw input
dsolve(x^2*diff(y(x),x) = (a*x+b*y(x))*y(x), y(x))
Maple raw output
[y(x) = x*(a-1)/(x^(-a)*_C1*x*a-x^(-a)*_C1*x-b)]