4.4.14 \(x y'(x)=a x-\left (1-b x^2\right ) y(x)\)

ODE
\[ x y'(x)=a x-\left (1-b x^2\right ) y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0093403 (sec), leaf count = 30

\[\left \{\left \{y(x)\to \frac {b c_1 e^{\frac {b x^2}{2}}-a}{b x}\right \}\right \}\]

Maple
cpu = 0.016 (sec), leaf count = 25

\[ \left \{ y \relax (x ) ={\frac {1}{bx} \left ({{\rm e}^{{\frac {b{x}^{2}}{2}}}}{\it \_C1}\,b-a \right ) } \right \} \] 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),'implicit')

Maple raw output

y(x) = (exp(1/2*b*x^2)*_C1*b-a)/b/x