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
=?

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

Generally

So

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

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

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

h= 12 inches

step-by-step explanation: