Find the solution of the given initial value problem. ty' + 6y = t2 − t + 1, y(1) = 1 6 , t > 0
1 answer
Question:
Find the solution of the given initial value problem. ty' + 6y = t2 − t + 1, y(1) = 1 6 , t > 0
Answers
Answer:Step-by-step explanation:Given is a differential equation as[tex]ty' + 6y = t^2 - t + 1, y(1) = 1 6 , t > 0[/tex]Divide this by t to get in linear form[tex]y'+6y/t = t-1+1/t[/tex]This is of the form y' +p(t) y = Q(t)where p(t) = 1/t[tex]e^(\int 1/tdt) = t[/tex]So solution would be[tex]yt = \int t^2-t+1 dt\\= t^3/3-t^2/2+t+C[/tex]siubstitute y(1) = 16[tex]16 = 16^3/3-128+1+C\\C = -1206[/tex]
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