ODE
\[ x^2 y'(x)=y(x) (a+b x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00621471 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_1 e^{-\frac {a}{x}} x^b\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{b}{{\rm e}^{-{\frac {a}{x}}}} \right \} \] Mathematica raw input
DSolve[x^2*y'[x] == (a + b*x)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (x^b*C[1])/E^(a/x)}}
Maple raw input
dsolve(x^2*diff(y(x),x) = (b*x+a)*y(x), y(x),'implicit')
Maple raw output
y(x) = _C1*x^b*exp(-1/x*a)