Question

Let $y=f(x),x\in R$ satisfies the differential equation $x\left(y^{\prime \prime }+y^{\prime }\right)=-y^{\prime }-e^{-x}$ and $y(0)=-1$ where $y^{\prime }=\frac{dy}{dx}$ and $y^{\prime \prime }=\frac{d^{2}y}{d{x}^2}$.
The value of ${\int }_0^1{e}^x(f(x)+3)dx$ is equal to

• A. e
• B. $e-1$
• C. 3
• D. 1

Answer 1

Answer: (A)

Correct answer is (a) e