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Answer:
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.