ODE
\[ x y'(x)=a x-\left (1-b x^2\right ) y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.173238 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {-a+b c_1 e^{\frac {b x^2}{2}}}{b x}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 26
\[\left [y \left (x \right ) = -\frac {a}{b x}+\frac {{\mathrm e}^{\frac {b \,x^{2}}{2}} \textit {\_C1}}{x}\right ]\] Mathematica raw input
DSolve[x*y'[x] == a*x - (1 - b*x^2)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-a + b*E^((b*x^2)/2)*C[1])/(b*x)}}
Maple raw input
dsolve(x*diff(y(x),x) = a*x-(-b*x^2+1)*y(x), y(x))
Maple raw output
[y(x) = -a/b/x+exp(1/2*b*x^2)/x*_C1]