## jje089 Group Title Solve the differential equation dT(t)/dt= 0.85(75+35sin(t)-T) one year ago one year ago

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!