Find the solution of the given initial value problem. ty' + 2y = sin t, y π 2 = 9, t > 0 y(t) =

For the ODE

multiply both sides by t so that the left side can be condensed into the derivative of a product:

Integrate both sides with respect to t :

Divide both sides by to solve for y :

Now use the initial condition to solve for C :

So the particular solution to the IVP is

or

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