Question

The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:

• A. \(y = x\log(x) - x + 2\)
• B. \(y = (x + 1)\log(x + 1) - x + 3\)
• C. \(y = (x + 1)\log(x + 1) + x - 3\)
• D. \(y = x\log(x) + x - 2\)

Hint:

When solving differential equations, verify the solution by substituting back into the original equation.