What is laplacetransform cos(3t+5)e^{2t} ?

The answer to laplacetransform cos(3t+5)e^{2t} is (cos(5)(s-2)-3sin(5))/((s-2)^2+9)

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laplacetransform cos(3t+5)e^{2t}

laplace transform

cos (3 t + 5) e^{2 t}

\frac{cos ( 5 ) ( s - 2 ) - 3 sin ( 5 )}{( s - 2 ) ^{2} + 9}

Solution steps

L {e^{2 t} cos (3 t + 5)}

Apply transform rule:

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

cos (3 t + 5) e^{2 t} : f (t) = cos (3 t + 5), a = 2

= L {cos (3 t + 5)} (s - 2)

L {cos (3 t + 5)} : \frac{cos ( 5 ) s - 3 sin ( 5 )}{s ^{2} + 9}

= \frac{cos ( 5 ) ( s - 2 ) - 3 sin ( 5 )}{( s - 2 ) ^{2} + 9}

What is laplacetransform cos(3t+5)e^{2t} ?
The answer to laplacetransform cos(3t+5)e^{2t} is (cos(5)(s-2)-3sin(5))/((s-2)^2+9)