Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.`y=a e^(3x)+b e^(-2x)`

Explanation

To form a differential equation representing the given family of curves \( y = a e^{3x} + b e^{-2x} \) by eliminating the arbitrary constants \( a \) and \( b \), we will follow these steps:

### Step 1: Differentiate the equation once with respect to \( x \).

Given:
\[ y = a e^{3x} + b e^{-2x} \]
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