Internal problem ID [2909]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 161.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -a x +\left (-b \,x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
dsolve(x*diff(y(x),x) = a*x-(-b*x^2+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a}{b x}+\frac {{\mathrm e}^{\frac {b \,x^{2}}{2}} c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 30
DSolve[x y'[x]==a x-(1-b x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-a+b c_1 e^{\frac {b x^2}{2}}}{b x} \\ \end{align*}