Question

On multiplying \[\frac{dy}{dx}-y=\cos x\] throughout by \[e^{-x}\], which equation is obtained?

Options

• \[e^{-x}\frac{dy}{dx}-e^{-x}y=e^{-x}\cos x\]

• \[e^{-x}\frac{dy}{dx}-y=\cos x\]

• \[e^{-x}\frac{dy}{dx}+e^{-x}y=e^{-x}\cos x\]

• \[e^{x}\frac{dy}{dx}-e^{x}y=e^{x}\cos x\]

Answer 1

Every term of the equation is multiplied by the integrating factor \[e^{-x}\]. Thus the sign of the \[y\]-term remains negative.