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.

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: