Answer to Question #175505 in Differential Equations for Usman

Question

y= e^mx

5(dy/dx) = 2y

Answer 1

Given that

$y = e^{mx}$

We have that

$\dfrac{dy}{dx} = me^{mx}$

Substituting into the equation, we have

$5me^{mx} = 2e^{mx}\\ 5me^{mx} -2e^{mx} = 0 \\ e^{mx}(5m-2) = 0$

Since $e^{mx} \neq 0$ , we have that

$5m-2 = 0\\ 5m=2\\ m = \frac{2}{5} = 0.4$

Hence, $y = e^{0.4x}$