The author considers the initial value problem for the integro-ordinary differential equation \(\epsilon y'+xy+\lambda \int^{b}_{a}K(x,s)y(s)ds=f(x)\), \(x\in [a,b]\), \(a0\) is a small parameter. She shows that under certain conditions the solution \(y=y(x,\epsilon)\) exists and \(y(x,\epsilon)\to y(x,0)\) as \(\epsilon\to 0\).