Simple ODE

[iaretheman]

I'm in an elementary Calculus class, but I'm stuck on a problem. It is:

y'(x) = (y-5)/x
Given y(0) = 5 and y(3) = -1

It's part four of a multi-part problem, and I'm feeling pretty dumb right about now. Any help?

 

[srmichael]

I'm in an elementary Calculus class, but I'm stuck on a problem. It is:

y'(x) = (y-5)/x
Given y(0) = 5 and y(3) = -1

It's part four of a multi-part problem, and I'm feeling pretty dumb right about now. Any help?

So you have \(\displaystyle \frac{dy}{dx}=\frac{y-5}{x}\). For these elementary differential equations your goal is to get all the y terms together and all the x terms together. So for this you would have:

\(\displaystyle \frac{dy}{y-5}=\frac{dx}{x}\)

Take the integrals of both sides and solve for y, using the initial points given to solve for a unique solution. Go for it and lets us know if you get stuck.