What is laplacetransform 5cos(2t)-3sin(3t) ?

The answer to laplacetransform 5cos(2t)-3sin(3t) is (5s)/(s^2+4)-9/(s^2+9)

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laplacetransform 5cos(2t)-3sin(3t)

laplace transform

5 cos (2 t) - 3 sin (3 t)

\frac{5 s}{s ^{2} + 4} - \frac{9}{s ^{2} + 9}

Solution steps

L {5 cos (2 t) - 3 sin (3 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)}

= 5 L {cos (2 t)} - 3 L {sin (3 t)}

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

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

= 5 \cdot \frac{s}{s ^{2} + 4} - 3 \cdot \frac{3}{s ^{2} + 9}

Refine

5 \frac{s}{s ^{2} + 4} - 3 \frac{3}{s ^{2} + 9} : \frac{5 s}{s ^{2} + 4} - \frac{9}{s ^{2} + 9}

= \frac{5 s}{s ^{2} + 4} - \frac{9}{s ^{2} + 9}

y^{^{''}} - \frac{6}{x} y^{^{'}} + \frac{10}{x ^{2}} y = 0

h \to 0 lim (\frac{h + 5 - 5}{h})

y = \frac{2}{1 - 3 x}, at x = - 1

\int \frac{x + 8}{x ^{2} + 9} d x

\int \frac{1}{x ^{2} - 400} d x

What is laplacetransform 5cos(2t)-3sin(3t) ?
The answer to laplacetransform 5cos(2t)-3sin(3t) is (5s)/(s^2+4)-9/(s^2+9)