# On singularly perturbed external differentiable equations with canards

Let $$X$$ be an internal set. A flexible function is a function $$F:X \rightarrow E$$. An internal function $$f: X\rightarrow R$$ is called a representative of $$F$$ if $$f(x)\in F(x)$$ for all $$x\in X$$. A flexible function $$F:X→E$$ is called internally representable if $$F=\{f∣f:X→ \mathbb{R}$$ representative of $$F$$} we study equation $$ε(\frac{dx}{dt})=tx+α$$ where $$ε$$ is an infinitesimal positive real number and $$α$$ is a neutrix.

How to solve this equation

$$\epsilon \frac{dx}{dt}=tx+\mathcal{L} \sqrt{\epsilon} e^{-A/\epsilon}$$, where $$A$$ is appreciable positive and $$\mathcal{L}$$ is the set of all limited numbers.