Solve for w(t) at t=100sec if dw/dt = 0.025 sec/w + 75 if w(0)=2.75.?

Question

Solve for w(t) at t=100s if dw/dt = 0.025 s^(-1) w + 75
if w(0)=2.75.

0.025 s^(-1) is a constant coefficient in front of w.


I need to show all work, and don't understrand Diferentaion and inergrals too well...so if you can solve this showing a step by step way to follow that will be greatly appreciated.

Answer 1

I believe your equation is missing a "t", so I have added it; dw/dt = 0.025t + 75

The integration to get w(t) is pretty straightforward:
w(t)= 1/2 (0.025) t^2+ 75t + C1
We can evaluate C1 by solving w(t) for the w(0) information: w(o)= C1 = 2.75
So we can solve by typical substiution, which I leave to you.