Approximation by First-Order Linear Differential Equations with an Initial Condition

Abstract EN

We will consider a continuously differentiable function y : I → R satisfying the inequality p t y ′ t - q t y t - r t ≤ ε for all t ∈ I and y t 0 - α ≤ δ for some t 0 ∈ I and some α ∈ R .

Then we will approximate y by a solution z of the linear equation p t z ′ t - q t z t - r ( t ) = 0 with z ( t 0 ) = α .