What is e^{-mt}(asin(wt)+bcos(wt)) ?

The solution to e^{-mt}(asin(wt)+bcos(wt)) is (bcos(tw)+asin(tw))/(e^{mt)}

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simplify e^{-mt}(asin(wt)+bcos(wt))

simplify

e^{- m t} (a sin (wt) + b cos (wt))

\frac{b cos ( tw ) + a sin ( tw )}{e ^{m t}}

Solution steps

e^{- m t} (a sin (wt) + b cos (wt))

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{m t}} (b cos (tw) + a sin (tw))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( a sin ( wt ) + b cos ( wt ) )}{e ^{m t}}

1 \cdot (a sin (wt) + b cos (wt)) = a sin (tw) + b cos (tw)

= \frac{a sin ( tw ) + b cos ( tw )}{e ^{m t}}

- 2.18 \cdot 1 0^{- 18} (1 - 0)

\frac{19}{3}

(1 + 3 y)^{- 2}

2^{x} 0. 5^{x}

\frac{( 3 ^{n} )}{( 2 ^{n} )}

What is e^{-mt}(asin(wt)+bcos(wt)) ?
The solution to e^{-mt}(asin(wt)+bcos(wt)) is (bcos(tw)+asin(tw))/(e^{mt)}