簡約 e^{-x}(C^1cos(2x)+C^2sin(2x))

解

簡約

e^{- x} (C^{1} cos (2 x) + C^{2} sin (2 x))

\frac{C cos ( 2 x ) + C ^{2} sin ( 2 x )}{e ^{x}}

解答ステップ

e^{- x} (C^{1} cos (2 x) + C^{2} sin (2 x))

指数の規則を適用する:

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

= \frac{1}{e ^{x}} (C^{1} cos (2 x) + C^{2} sin (2 x))

規則を適用

a^{1} = a

C^{1} = C

= \frac{1}{e ^{x}} (C cos (2 x) + C^{2} sin (2 x))

分数を乗じる:

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

= \frac{1 \cdot ( C cos ( 2 x ) + C ^{2} sin ( 2 x ) )}{e ^{x}}

1 \cdot (C cos (2 x) + C^{2} sin (2 x)) = C cos (2 x) + C^{2} sin (2 x)

= \frac{C cos ( 2 x ) + C ^{2} sin ( 2 x )}{e ^{x}}