Consider the differential equation
dxdy=yx−3,
where the particular solution satisfies y(5)=2.
(a) Solve for y explicitly in terms of x. Show all steps leading to your result.
(b) Determine the maximal open interval on which your explicit solution is valid. Explain how every restriction encountered in your work leads to the stated interval.
(c) Verify that your solution satisfies both the differential equation and the initial condition for every x in the interval you provided.