4.6.7 \(x^2 y'(x)=y(x) (a+b x)\)

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

\[ \left \{ y \relax (x ) ={\it \_C1}\,{x}^{b}{{\rm e}^{-{\frac {a}{x}}}} \right \} \] 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)