Find the differential equation corresponding to `y=a e^(2x)+b e^(-3x)+c e^x` where `a ,\ b ,\ c` are arbitrary constants.

Explanation

To find the differential equation corresponding to the function \( y = a e^{2x} + b e^{-3x} + c e^{x} \), where \( a, b, c \) are arbitrary constants, we will follow these steps:

### Step 1: Differentiate the function
We start by differentiating \( y \) with respect to \( x \):

\[ \frac{dy}{dx} = \frac{d}{dx}(a e^{2x}) + \frac{d}{dx}(b e^{-3x}) + \frac{d}{dx}(c e^{x}) \]
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