Determine if the given function y=f(x) is a solution of the accompanying differential equation.

Question

y′ + y = e^2x

y = 9e^-x + e^2x

Answer 1

Explanation:



Given y = 9e^-x + e^2x

Differentiate w.r.t x

y' = -9e^-x + e^2x

We have to show y' + y = e^2x .........(A)

Put values of y & y' in (A)

-9e^-x +2e^2x+9e^-x+e^2x = e^2x

3e^2x≠ e^2x

Didn't satisfy the equation

Hence, given y=9e^-x+e^2x is not a solution of the given differential equation.

Answer 2

If y = 9e^-x + e^2x, then y' + y = -9e^-x + 2e^2x ≠ e^2x

So, y = e^2x is not a solution of the given differential equation.