What is factor C_{1}e^x+C_{2}e^{-x} ?

The solution to factor C_{1}e^x+C_{2}e^{-x} is e^{-x}(e^{2x}C_{1}+C_{2})

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factor C_{1}e^x+C_{2}e^{-x}

factor

C_{1} e^{x} + C_{2} e^{- x}

e^{- x} (e^{2 x} C_{1} + C_{2})

Solution steps

C_{1} e^{x} + C_{2} e^{- x}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{x} = e^{- x} e^{2 x}

= C_{1} e^{- x} e^{2 x} + C_{2} e^{- x}

Factor out common term

e^{- x}

= e^{- x} (C_{1} e^{2 x} + C_{2})

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What is factor C_{1}e^x+C_{2}e^{-x} ?
The solution to factor C_{1}e^x+C_{2}e^{-x} is e^{-x}(e^{2x}C_{1}+C_{2})