What is (d^2)/(dx^2)(({y}(x,C))(Ce^{-x}+Ce^{2x})) ?

The answer to (d^2)/(dx^2)(({y}(x,C))(Ce^{-x}+Ce^{2x})) is

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(d^2)/(dx^2)(({y}(x,C))(Ce^{-x}+Ce^{2x}))

\frac{d ^{2}}{d x ^{2}} ((y (x, C)) (C e^{- x} + C e^{2 x}))

(\frac{d ^{2}}{d x ^{2}} (y (x, C)) (C e^{- x} + C e^{2 x}) + (- C e^{- x} + C e^{2 x} \cdot 2) \frac{d}{d x} (y (x, C))) + ((C e^{- x} + 4 C e^{2 x}) y (x, C) + \frac{d}{d x} (y (x, C)) (- C e^{- x} + C e^{2 x} \cdot 2))

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y (x, C)) (C e^{- x} + C e^{2 x}))

\frac{d}{d x} (y (x, C) (C e^{- x} + C e^{2 x})) = \frac{d}{d x} (y (x, C)) (C e^{- x} + C e^{2 x}) + (- C e^{- x} + C e^{2 x} \cdot 2) y (x, C)

= \frac{d}{d x} (\frac{d}{d x} (y (x, C)) (C e^{- x} + C e^{2 x}) + (- C e^{- x} + C e^{2 x} \cdot 2) y (x, C))

\frac{d}{d x} (\frac{d}{d x} (y (x, C)) (C e^{- x} + C e^{2 x}) + (- C e^{- x} + C e^{2 x} \cdot 2) y (x, C)) = (\frac{d ^{2}}{d x ^{2}} (y (x, C)) (C e^{- x} + C e^{2 x}) + (- C e^{- x} + C e^{2 x} \cdot 2) \frac{d}{d x} (y (x, C))) + ((C e^{- x} + 4 C e^{2 x}) y (x, C) + \frac{d}{d x} (y (x, C)) (- C e^{- x} + C e^{2 x} \cdot 2))

= (\frac{d ^{2}}{d x ^{2}} (y (x, C)) (C e^{- x} + C e^{2 x}) + (- C e^{- x} + C e^{2 x} \cdot 2) \frac{d}{d x} (y (x, C))) + ((C e^{- x} + 4 C e^{2 x}) y (x, C) + \frac{d}{d x} (y (x, C)) (- C e^{- x} + C e^{2 x} \cdot 2))

\frac{( - 1 ) ^{n} n !}{6 ^{n} ( n + 2 )}

\frac{( - a ( n ) ^{3} + a ( n ) \cdot ( 1 + 6 n ) )}{6}

12 (\frac{x - 4}{4} + \frac{x}{3} = \frac{6}{1})

(z + 3)^{2}

\frac{( - x ^{2} - 64 )}{( x ^{2} - 64 ) ^{2}}

What is (d^2)/(dx^2)(({y}(x,C))(Ce^{-x}+Ce^{2x})) ?
The answer to (d^2)/(dx^2)(({y}(x,C))(Ce^{-x}+Ce^{2x})) is