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

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

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

laplace transform

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

\frac{cos ( 5 )}{( s - 2 ) ^{2}}

Solution steps

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

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= cos (5) L {e^{2 t} t}

L {e^{2 t} t} : \frac{1}{( s - 2 ) ^{2}}

= cos (5) \frac{1}{( s - 2 ) ^{2}}

Refine

cos (5) \frac{1}{( s - 2 ) ^{2}} : \frac{cos ( 5 )}{( s - 2 ) ^{2}}

= \frac{cos ( 5 )}{( s - 2 ) ^{2}}

e^{2 x}, e^{6 x}, x = 1

\frac{d}{d x} (- 2 x - 4)

x \to 1 lim (\frac{cos ( π x )}{3})

f^{^{'}} (x) = e^{3 x + 2} - 3 x^{2}

\int x y^{2} - x^{2} d x

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