What is (d^2)/(dx^2)(({y}(x,s))(c*e^{2x}+s*xe^{2x})) ?

The answer to (d^2)/(dx^2)(({y}(x,s))(c*e^{2x}+s*xe^{2x})) is

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(d^2)/(dx^2)(({y}(x,s))(ce^{2x}+sxe^{2x}))

\frac{d ^{2}}{d x ^{2}} ((y (x, s)) (c \cdot e^{2 x} + s \cdot x e^{2 x}))

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

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y (x, s)) (c e^{2 x} + s x e^{2 x}))

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

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

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

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

(e^{2 x} + e^{3 x})^{2}

\frac{2 ( - x - 4 )}{( x - 2 ) ^{4}}

(x + 4) (2 x + 3)

\frac{1}{( x + 8 ) ^{2}}

x^{2} (x + 3) e^{x}

What is (d^2)/(dx^2)(({y}(x,s))(c*e^{2x}+s*xe^{2x})) ?
The answer to (d^2)/(dx^2)(({y}(x,s))(c*e^{2x}+s*xe^{2x})) is