Question

Solve the differential equation dy/dx = 5-y?

Answer 1

I know if it was x I would just integrate, but with this y do I just send it over to the other side?

Answer 2

that's a separable DE....
dy/dx = 5-y ---> \(\large \frac{dy}{5-y}=dx \)
now just integrate both sides...

Answer 3

u = 5-y
du = -1

so it could be -integral of u'/u = dx

Answer 4

but they want in terms of y soo.... hmm

Answer 5

I will give you some example:
dy/dx=5y with initial condition y(0)=2?

dy/dx = 5y
INT (1/y) dy = INT 5 dx
ln(y) = 5x + c
y = e^(5x + c) = a*e^(5x)

y(0) = 2, 2 = a*e^0 = a
y = 2e^(5x)

Answer 6

but if you multiply and divide the y term for (-1) in the numerator you have the derivative of the denominator so you can put as
-Ln(5-y)=x+C
you take exponentials at both sides...