What is e^{-20t}(C_{1}cos(10t)+C_{2}sin(10t)) ?

The solution to e^{-20t}(C_{1}cos(10t)+C_{2}sin(10t)) is (C_{1}cos(10t)+C_{2}sin(10t))/(e^{20t)}

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simplify e^{-20t}(C_{1}cos(10t)+C_{2}sin(10t))

simplify

e^{- 20 t} (C_{1} cos (10 t) + C_{2} sin (10 t))

\frac{C _{1} cos ( 10 t ) + C _{2} sin ( 10 t )}{e ^{20 t}}

Solution steps

e^{- 20 t} (C_{1} cos (10 t) + C_{2} sin (10 t))

Apply exponent rule:

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

= \frac{1}{e ^{20 t}} (C_{1} cos (10 t) + C_{2} sin (10 t))

Multiply fractions:

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

= \frac{1 \cdot ( C _{1} cos ( 10 t ) + C _{2} sin ( 10 t ) )}{e ^{20 t}}

1 \cdot (C_{1} cos (10 t) + C_{2} sin (10 t)) = C_{1} cos (10 t) + C_{2} sin (10 t)

= \frac{C _{1} cos ( 10 t ) + C _{2} sin ( 10 t )}{e ^{20 t}}

0.05 \cdot 1 0^{- 3} \cdot (\frac{- 8 \cdot \frac{0.1}{2}}{0. 1 ^{2}})

0.00246 \cdot 0.85 \cdot 5.67 \cdot 1 0^{- 8} \cdot (62 3^{4} - 29 8^{4})

(x - x^{2})^{- 6}

1.02 (lo g_{10} (308000))^{- 2.5}

[(- 7)^{5}]^{3}

What is e^{-20t}(C_{1}cos(10t)+C_{2}sin(10t)) ?
The solution to e^{-20t}(C_{1}cos(10t)+C_{2}sin(10t)) is (C_{1}cos(10t)+C_{2}sin(10t))/(e^{20t)}