Question: ProblemsIn problem 1-5, find the general solution of the given differential equation, or solve the given initial valueproblem.[2pts]y'=2y+3.[2pts]y'+3y-5=0,y(0)=1.[2pts]y'+3y=2te-3t.[2pts]ty'+2y=t2-t+1,y(1)=2,t>0.[2pts]y'+12y=1+2cos(2t),y(0)=0.In Problem 6, find the value ofy0 for

ProblemsIn problem 1-5, find the general solution of the given differential equation, or solve the given initial valueproblem.[2pts]y'=2y+3.[2pts]y'+3y-5=0,y(0)=1.[2pts]y'+3y=2te-3t.[2pts]ty'+2y=t2-t+1,y(1)=2,t>0.[2pts]y'+12y=1+2cos(2t),y(0)=0.In Problem 6, find the value ofy0 for which the solution of the following initial value problem remains finite ast.[2pts]y'-y=2+3sint,y(0)=y0.

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