Show that the function y = e^(-x) + 2 is a solution of the differential equation dy/dx + y = 2.

Question

Show that the function y = e^-x + 2 is a solution of the differential equation \(\frac{dy}{dx}\) + y = 2.

Answer 1

The given function is

y = e^-x + 2

Differentiating equation (1) w.r.t 'x', we get

\(\frac{dy}{dx}\) = - e^-x

From equations (1) and (2), we get

Thus, the function y = e^-x + 2 is the solution of the differential equation \(\frac{dy}{dx}\) + y = 2.

Hence Proved.