Find all values of m so that the function y= e^mx is a solution of the given differential equation. y' + 2y =0

m = - 2 is the value of m that the function y= e^mx is a solution of the differential equation, y' + 2y = 0.

Step-by-step explanation:

To determine all values of m so that the function y= e^mx is a solution of the given differential equation.

First, we will find y'.

From, y= e^mx

But,

Hence,

∴

Now, we will put the values of y' and y into the given differential equation y' + 2y =0

From the question,

and

Then, becomes

Then,

∴

Hence, m = - 2 is the value of m that the function y= e^mx is a solution of the differential equation, y' + 2y = 0.

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step-by-step explanation: