How can the following differential equation can be solved? $$ \frac{dy}{dt}=3+e^{-t} -\frac{1}{2}y $$ I proceeded by by rearranging the equation as follows $$ \frac{dy}{dt}+\frac{1}{2}y=3+e^{-t} $$My idea was to make the LHS a derivatives of two variables so that it could be integrated. But apparently I could not do that. How should i proceed now?
Your help is much appreciated.Thankyou.
How to solve the differential equation?
5
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calculus
ordinary-differential-equations
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0If $y$ is a solution, then multiplying by $e^{\frac t2}$ we have $\dfrac{d(y(t)e^{\frac t2})}{dt} =3e^{\frac t2}+e^{-\frac t2}$. – 2011-07-23
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0@nihilisticgeek: please see: Earl A. Coddington: _An Introduction to Ordinary Differential Equations_, p39. It can be very useful. – 2011-07-25