What is e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t)) ?

The solution to e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t)) is (c_{1}cos(60t)+c_{2}sin(60t))/(e^{20t)}

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simplify e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t))

simplify

e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

\frac{c _{1} cos ( 60 t ) + c _{2} sin ( 60 t )}{e ^{20 t}}

Solution steps

e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

Apply exponent rule:

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

= \frac{1}{e ^{20 t}} (c_{1} cos (60 t) + c_{2} sin (60 t))

Multiply fractions:

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

= \frac{1 \cdot ( c _{1} cos ( 60 t ) + c _{2} sin ( 60 t ) )}{e ^{20 t}}

1 \cdot (c_{1} cos (60 t) + c_{2} sin (60 t)) = c_{1} cos (60 t) + c_{2} sin (60 t)

= \frac{c _{1} cos ( 60 t ) + c _{2} sin ( 60 t )}{e ^{20 t}}

4 π \cdot 1 0^{- 7} \cdot \frac{200 \cdot 0 , 10}{0.0005}

4.78 \cdot 1 0^{- 6} \cdot 101

5 - x \cdot x^{2} - 9

a \cdot a + 1

a^{2} x b^{2} (a = 5, b = 2)

What is e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t)) ?
The solution to e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t)) is (c_{1}cos(60t)+c_{2}sin(60t))/(e^{20t)}