Verify by substitution that the given function is a solution of the given diflerental equation. Note that any primes denote derivatives with respect to $x.$

$Y^{\text{'}}=y2e^{-x},y=5e^x-e^{-x}$

What step should roa tabe to wenty theit the furction is a sclution to the given differential equation?

A$.$ Determine the frict ard scoond Serivalives of the geven function and substitute rito the delerental equation

$$ Integrate the lunction and substitse into the diflerential equation

Differentiato the given function and substitue into the atterential equation.

Substitue the green furcion info the differential equation.

Integrato or afferentiabe fee firction as reeded. Select the correct choice below and fill nary answer boxes within your choice.

A$.$ The first derivative is $x^{\text{'}}=$ and the second denialive is $y^{\text{'}\text{'}}=$

B$.$ The nabline niegral of fill function e ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ydx=$

$$ c$.$ The frut derivative is ${}^{\text{'}}=$

$$ D$.$ The function dies not need $k$ i be integratiod or afferentiabod to werity that if is a sobtion to the differential equilion