3.46: Vector ratio in triangle $OAB$

In triangle $OAB$, $C$ is the mid-point of $OA$, and $D$ on $CB$ satisfies $\overrightarrow{CD}:\overrightarrow{DB}=2:3$. Given $\overrightarrow{OC}=\mathbf{c}$ and $\overrightarrow{CB}=\mathbf{b}$, the point $E$ on $AB$ satisfies $\overrightarrow{OE}=m\overrightarrow{OD}$ and $\overrightarrow{AE}=n\overrightarrow{AB}$.

Find two expressions for $\overrightarrow{OE}$ and hence find $\dfrac{AE}{EB}$.