Question

Someone please help it’s overdue !!

Answer 1

Explanation:

a. separate the variables

`\frac{\mathrm{d} y}{\mathrm{d} x}` = 500-y

dy/(500-y) = dx

b. integrating your equation in part a to find the general equation of

differential

Integrating on both sides

`\int`dy/(500-y) =
`\int`dx

-㏑(500-y) = x +C ..............(1)

where C is constant of integration

c. If y(0) = 7

putting in equation (1)

-㏑(500-7) = 0+C

C = -㏑493

d. The particular solution is

-㏑(500-y) = x -㏑473

㏑473/(500-y) = x

473 = (500-y)
`e^x`