Solve the differential equation $\frac{dy}{dx} + y = x$.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) →$xe^x - e^x + c $ ##
The given differential equation is of the form $\frac{dy}{dx} + Py = Q$. The integrating factor of the differential equation is $e^{\int dx} = e^x$.
The solution of the differential equation is
$ ye^x = \int xe^x dx + c $
$ = xe^x - e^x + c $