What is laplacetransform (cos(7t))/(e^{5t)} ?

The answer to laplacetransform (cos(7t))/(e^{5t)} is (s+5)/((s+5)^2+49)

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laplacetransform (cos(7t))/(e^{5t)}

laplace transform

\frac{cos ( 7 t )}{e ^{5 t}}

\frac{s + 5}{( s + 5 ) ^{2} + 49}

Solution steps

L {\frac{cos ( 7 t )}{e ^{5 t}}}

Apply transform rule:

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

then

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

For

\frac{cos ( 7 t )}{e ^{5 t}} : f (t) = cos (7 t), a = - 5

= L {cos (7 t)} (s + 5)

L {cos (7 t)} : \frac{s}{s ^{2} + 49}

= \frac{( s + 5 )}{( s + 5 ) ^{2} + 49}

= \frac{s + 5}{( s + 5 ) ^{2} + 49}

x \frac{d y}{d x} + y = y^{2} x^{2} ln (x)

\frac{d}{d x} (sin^{2} (π x))

\int x^{- 8} d x

t an g e n t y = \frac{x}{1 + x ^{2}}, at x = 0

t a y l or e^{x} \cdot sin (x)

What is laplacetransform (cos(7t))/(e^{5t)} ?
The answer to laplacetransform (cos(7t))/(e^{5t)} is (s+5)/((s+5)^2+49)