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

The answer to laplacetransform 2sin(3t)+5cos(3t) is 6/(s^2+9)+(5s)/(s^2+9)

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

laplace transform

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

\frac{6}{s ^{2} + 9} + \frac{5 s}{s ^{2} + 9}

Solution steps

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

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

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

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

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

Refine

2 \frac{3}{s ^{2} + 9} + 5 \frac{s}{s ^{2} + 9} : \frac{6}{s ^{2} + 9} + \frac{5 s}{s ^{2} + 9}

= \frac{6}{s ^{2} + 9} + \frac{5 s}{s ^{2} + 9}

y^{^{''}} + 13 y = 0

\frac{d y}{d x} = \frac{x + x y ^{2}}{4 y}

\int_{0}^{\frac{3 π}{2}} cos^{3} (17 x) d x

y = x + 1, x = 8

\int x^{2} - 2 x + 2 d x

What is laplacetransform 2sin(3t)+5cos(3t) ?
The answer to laplacetransform 2sin(3t)+5cos(3t) is 6/(s^2+9)+(5s)/(s^2+9)