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Popular >

laplacetransform e^{5t}(-2cos(t)+12sin(t))

Solution

laplace transform

e^{5 t} (- 2 cos (t) + 12 sin (t))

Solution

- \frac{2 ( s - 5 )}{( s - 5 ) ^{2} + 1} + \frac{12}{( s - 5 ) ^{2} + 1}

Solution steps

L {e^{5 t} (12 sin (t) - 2 cos (t))}

Apply transform rule:

if

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

e^{5 t} (- 2 cos (t) + 12 sin (t)) : f (t) = (- 2 cos (t) + 12 sin (t)), a = 5

= L {(- 2 cos (t) + 12 sin (t))} (s - 5)

L {(- 2 cos (t) + 12 sin (t))} : - \frac{2 s}{s ^{2} + 1} + \frac{12}{s ^{2} + 1}

= - \frac{2 ( s - 5 )}{( s - 5 ) ^{2} + 1} + \frac{12}{( s - 5 ) ^{2} + 1}

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Frequently Asked Questions (FAQ)

What is laplacetransform e^{5t}(-2cos(t)+12sin(t)) ?
The answer to laplacetransform e^{5t}(-2cos(t)+12sin(t)) is -(2(s-5))/((s-5)^2+1)+(12)/((s-5)^2+1)