Question

Find the value of m so that the functiony=emx is a solution of the differential equation y′+2y=0

Answer 1

Answer on Question #69652 – Math – Differential Equations

Question

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

$$y' + 2y = 0$$

Solution

$$y' = m e^{mx}$$ $$m e^{mx} + 2 e^{mx} = 0$$ $$e^{mx}(m + 2) = 0$$ $$e^{mx} \neq 0, \text{ so}$$ $$m = -2$$

Answer: $m = -2$.

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