What is laplacetransform f(t)=cos(5t)+sin(2t) ?

The answer to laplacetransform f(t)=cos(5t)+sin(2t) is s/(s^2+25)+2/(s^2+4)

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laplacetransform f(t)=cos(5t)+sin(2t)

laplace transform

f (t) = cos (5 t) + sin (2 t)

\frac{s}{s ^{2} + 25} + \frac{2}{s ^{2} + 4}

Solution steps

L {cos (5 t) + sin (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 {cos (5 t)} + L {sin (2 t)}

L {cos (5 t)} : \frac{s}{s ^{2} + 25}

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

= \frac{s}{s ^{2} + 25} + \frac{2}{s ^{2} + 4}

y^{^{''}} - y = 0, y (0) = 6

\int \frac{x}{( 1 + x ^{2} )} d x

x \to - 1 lim (\frac{x ^{3} + 1}{x - 1})

\int \frac{x ^{2}}{( x ^{2} + 1 )} d x

1 - 1 e^{(- t - 2)}

What is laplacetransform f(t)=cos(5t)+sin(2t) ?
The answer to laplacetransform f(t)=cos(5t)+sin(2t) is s/(s^2+25)+2/(s^2+4)