Question

Find the value of
m
so that the function
y=e^mx
is a solution of the differential equation
y′+2y=0

a=0
b=3
c=1
d=2

Answer 1

Answer on question #77918 – Math – Differential Equations

Question

Find the value of $m$ so that the function $y = e^{mx}$ is a solution of the differential equation

$$y' + 2y = 0.$$ $$a = 0; \; b = 3; \; c = 1; \; d = 2.$$

Solution

Find the derivation of the given function:

$$y' = m e^{mx}.$$

Under the statement of the problem the function satisfies the differential equation so we have:

$$m e^{mx} + 2 e^{mx} = 0;$$ $$e^{mx}(m + 2) = 0;$$ $$m = -2.$$

P.S. There is no right answer among the suggested ones. Supposing that minus has been lost, the most close to the right answer is d.

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