Example 4.2: integrating factor Consider the first-order linear differential equation for the function y(t):

where b is a constant and g (t) is a given function. Now multiply through by the integrating factor ebt. We can show that d dt ebty

and the left-hand side is rendered a perfect differential, by virtue of our knowing the proper integrating factor. Now we are in position to solve the differential equation by integrating each side:


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