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.