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Solve D Using Laplace transform to solve initial value problem: D.E to A.E., solving A.E., then find

`L^(-1){F(s)}`

(a).

`x^('')+4x=sin2t,x(0)=x^(')(0)=0`

. (b).

`x^(')=4x+2y,y^(')=3x-y;x(0)=3,y(0)=-2`

; (c).

`tx^('')-2x^(')+tx=0,x(0)=0`

. (d).

`tx^('')-2x^(')+tx=0,x(0)=1`

. (f)* Can you find the general solution to

`tx^('')-2x^(')+tx=0`

?