Question

Using the differential equation dy/dx = 7 − y, find the intervals on the y-axis on which a nonconstant solution y = (x) is increasing. Find the intervals on the y-axis on which y = (x) is decreasing. PLEASE HELP!! Thanks!

Answer 1

I m not sure if i am right.. but also quite sure :P
first of all u do integration on both the left hand side and right hand side of the equation
so u will get:

\[\int\limits_{}^{}dy + y = \int\limits_{}^{} 7 dx\]
\[y+ \frac{ y^2 }{ 2 } = 7x + c (constant)\]

Answer 2

from there onwards u shud can figure out