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Solve the Initial Value Problem: dydx+2y=9,         y(0)=0 dydx+ycosx=5cosx,        y(0)=7d Find the general solution, y(t)y(t), which solves...

Solve the Initial Value Problem:

  1. dydx+2y=9,         y(0)=0
  2. dydx+ycosx=5cosx,        y(0)=7d
  1. Find the general solution, y(t)y(t), which solves the problem below, by the method of integrating factors.

8tdydt+y=t3,t>08tdydt+y=t3,t>0


Put the problem in standard form.
Then find the integrating factor, μ(t)=μ(t)=  ,__________
and finally find y(t)=y(t)= __________ . (use C as the unkown constant.)

  1. Solve the following initial value problem:

tdydt+6y=7ttdydt+6y=7t

with y(1)=2.y(1)=2.
Put the problem in standard form.
Then find the integrating factor, ρ(t)=ρ(t)= _______ ,
and finally find y(t)=y(t)= _________ .

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