Question 14(a)

Question 14(a)

Find the domain and range of the function that is the solution to the differential equation $\frac{dy}{dx} = e^{x+y}$ and whose graph passes through the origin

Solution

We rearrange the differential equation to

$$\begin{aligned} \frac{dy}{dx} = e^{x+y} \\ e^{-y}\frac{dy}{dx} = e^x \\ \end{aligned}$$

and find some function $u$ such that $\frac{du}{dy} = e^{-y}$

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