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Social ScienceFind the general solution of the differential equationy' + y = te-t + etand use it to determine how solutions behave as t → ∞.
Find the general solution of the differential equation
y' + y = te-t + et
and use it to determine how solutions behave as t → ∞.
Expert Answer
The differential equation is given as
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yytee
Use method of integrating factor such that the given differential equation is compared to the general equation:
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y'P(t)y(t) [(t)e!4 The solution is given as ye2 dt C Here, P(t1 and Q(t) =te" +e' The integrating factor is obtained as e*i e. ldt = e
Obtain the solution...
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C ye (t+e)dt +C t2e2 C 2 ye' 2 2r C (Divide by e' y = 2e 2e e' t2e* That is, y2e + e' 2
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