another differential equation

**crafty** · February 3rd 2009, 02:52 PM

(dy/dt) + y = cos (e^t)??? how???

**Danny** · February 3rd 2009, 02:55 PM

Originally Posted by crafty

(dy/dt) + y = cos (e^t)??? how???

Integrating factor

$\mu = e^t$

so

$\frac{d}{dt} \left( e^t y \right) = e^t \cos e^t$

$\int d \left( e^t y \right) = \int e^t \cos e^t\, dt + c$

I trust you can do the rest.

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