What is laplacetransform sin(2t)+cos(2t) ?

The answer to laplacetransform sin(2t)+cos(2t) is 2/(s^2+4)+s/(s^2+4)

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laplacetransform sin(2t)+cos(2t)

laplace transform

sin (2 t) + cos (2 t)

\frac{2}{s ^{2} + 4} + \frac{s}{s ^{2} + 4}

Solution steps

L {sin (2 t) + cos (2 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {sin (2 t)} + L {cos (2 t)}

L {sin (2 t)} : \frac{2}{s ^{2} + 4}

L {cos (2 t)} : \frac{s}{s ^{2} + 4}

= \frac{2}{s ^{2} + 4} + \frac{s}{s ^{2} + 4}

\int sin^{3} (3 θ) cos (3 θ) d θ

x y^{^{'}} + y = - 2 x y^{2}, y (1) = - 3

\frac{d}{d x} (\frac{4}{11 - x})

y = x 2 x + 3

\int 7^{x} tan (7^{x}) d x

What is laplacetransform sin(2t)+cos(2t) ?
The answer to laplacetransform sin(2t)+cos(2t) is 2/(s^2+4)+s/(s^2+4)