Verify that `y=c x+2c^2` is a solution of the differential equation `2((dy)/(dx))^2+x(dy)/(dx)-y=0.`

Explanation

To verify that \( y = cx + 2c^2 \) is a solution of the differential equation \( 2\left(\frac{dy}{dx}\right)^2 + x\frac{dy}{dx} - y = 0 \), we will follow these steps:

### Step 1: Differentiate \( y \) with respect to \( x \)

Given:
\[ y = cx + 2c^2 \]
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