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(D3+D2−21D−45)y=0r3+r2−21r−45=0r3−5r2+6r2−30r+9r−45=0r2(r−5)+6r(r−5)+9(r−5)=0(r−5)(r2+6r+9)(r−5)(r2+2(r)(3)+(3)2)(r−5)(r+3)2=0r−5=0 (r+3)2=0r=5 r+3=0,r+3=0r=−3−3y=c1e5x+(c2+c3x)e−3x
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laplace transform of 2[t] where  is greatest integer function <=t
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Solve the initial value problem below using the method of Laplace transforms.y8y′+41y=29e2ty(0)=1,y′(0)=7
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