Question

Solve the differential equation

dT(t)/dt= 0.85(75+35sin(t)-T)

Answer 1

This is a first order DE, and can be rewritten as:
\[T'+0.85T=29.75\sin t+63.75\]
In order to make this ODE separable, we multiply by the integrating factor [ http://en.wikipedia.org/wiki/Integrating_factor ]
The integrating factor here is \(\large e^{\int0.85dt}=e^{0.85t}\). Multiply both sides by the integration factors, you get:

\[e^{0.85t}T'+0.85e^{0.85t}T=e^{0.85t}(29.75\sin t+63.75).\]
This is equivalent to:
\[\frac{d}{dt} (e^{0.85t}T)=e^{0.85t}(29.75\sin t+63.75).\]
Integrate both sides and you're done!

Answer 2

Great thanks!!!