Finding m for Solution of Differential Equation y = e^{mx}

[KillerZ]

Homework Statement

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

Homework Equations

$$y = e^{mx}$$
$$5y^{'} = 2y$$

The Attempt at a Solution

I am not sure if this is right:

$$y^{'} = me^{mx}$$

$$5y^{'} = 5me^{mx}$$
$$2y = 2e^{mx}$$

$$2e^{mx} = 5me^{mx}$$

$$2 = 5m$$

$$m = 2/5$$

 

[Mark44]

Check it and see. You've already done all the hard work, and checking is a simple matter of seeing whether y = e^2x/5 satisfies your differential equation.

 

[KillerZ]

Ok, Thank you.