Question

Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for the solution.
9y' + y = 0; y = e-x/9
When
y = e-x/9,
y'= ?
Thus, in terms of x,
9y' + y = ? + e-x/9
=?

Answer 1

Answer:

The  result of the verification is : The indicated function is an explicit solution of the given differential equation

Step-by-step explanation:

From the question we are told that

The  given differential equation is  9y' + y = 0

  The  indicate solution is $y = e^{-\frac{x}{9} }$

Generally $y' =  -\frac{1}{9} e^{-\frac{x}{9} }$

So

    $9( -\frac{1}{9} e^{-\frac{x}{9} }) + e^{-\frac{x}{9} } =0$

For the  indicated function to be explicit solution of the given differential equation then the RHS and LHS of the above equation must be that same

      $- e^{-\frac{x}{9} } + e^{-\frac{x}{9} } =0$

      $0=0$

Thus result of the verification is : The indicated function is an explicit solution of the given differential equation