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

Explanation

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

### Step 1: Differentiate the given equation
We start with the equation:
\[ y = e^{2x}(a + bx) \]
Now, we differentiate this equation with respect to \( x \):
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