Question

Using separation of variables technique, solve the following differential equation with the given initial condition
y’ = -4y + 36 and y(2) = 10.
(Hint: Factor first!)

The solution is: (see attachment)

Answer 1

what do you have after factoring?

Answer 2

whoever is typing please do not give the answer

Answer 3

hey first separate out the terms such that dy and y are on the same side and similarly forx

Answer 4

alright so y'=-4(y-9) and this is dy/dx =-4(y-9) and this is equal to (1/(y-9))dy=-4dx integrate both sides is ln|y-9|=-4x +c and using y(2) = 10 y=10, x = 2 sub it in to find our c value

so in this case it is ln(1) = -8+c so this implies c=-2 sub it in you get ln|y-9|=-4x + 8 so your answer is B

Answer 5

u get 4dx= dy/(9-y) now integrate both sides to get the general solution and the use y(2)=10
@hamza_b23 is right

Answer 6

ok yea I just got -4(y - 9) when I was factoring it out. Anyways, thanks for solving it.

Answer 7

:)