Linear Differential Equation: Solving for M with Integrating Factor of .5

[HerpaDerp]

Homework Statement

dM/dT = .5m-24

I know this is a linear differential equation, with an integrating factor of .5
I get my final answer to be M = 48+ke^(-.5t)

Next, when t = 0, M = 7e^(.5t)...

Giving me k = 7e^(.5t) - 48

so to solve for M..

M = 48 + (7e^(.5t)-48)e^(-.5t)

And finally I get 55-48e^(-.5t)=M which I guess isn't right. Anyone help out what I did wrong here?



My final answer that I get is 55-48e^(-.5t), which I guess is wrong. Where did I go wrong?

 

[Dick]

The equation is separable. You don't really need an integrating factor. M=48+ke^(-.5t) is close, but you do you get the (-.5) factor in front of the t? That's wrong. And M=7*e^(.5t) at t=0 is kind of an odd way to state an initial condition. Do you mean M=7 at t=0?