What is laplacetransform 3sin(t)-3cos(t) ?

The answer to laplacetransform 3sin(t)-3cos(t) is 3/(s^2+1)-(3s)/(s^2+1)

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laplacetransform 3sin(t)-3cos(t)

laplace transform

3 sin (t) - 3 cos (t)

\frac{3}{s ^{2} + 1} - \frac{3 s}{s ^{2} + 1}

Solution steps

L {3 sin (t) - 3 cos (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)}

= 3 L {sin (t)} - 3 L {cos (t)}

L {sin (t)} : \frac{1}{s ^{2} + 1}

L {cos (t)} : \frac{s}{s ^{2} + 1}

= 3 \cdot \frac{1}{s ^{2} + 1} - 3 \cdot \frac{s}{s ^{2} + 1}

Refine

3 \frac{1}{s ^{2} + 1} - 3 \frac{s}{s ^{2} + 1} : \frac{3}{s ^{2} + 1} - \frac{3 s}{s ^{2} + 1}

= \frac{3}{s ^{2} + 1} - \frac{3 s}{s ^{2} + 1}

f (x) = \frac{4 + x}{x - 2}, at x = 8

x y y^{^{'}} = x^{2} + 3 y^{2}

3 x, x 64 - x^{2}

\int x^{\frac{7}{8}} d x

\frac{4 x ^{2} + 72 x}{x - 2}

What is laplacetransform 3sin(t)-3cos(t) ?
The answer to laplacetransform 3sin(t)-3cos(t) is 3/(s^2+1)-(3s)/(s^2+1)