Consider the differential equation:
dy/dx + 2xy = y + 4x − 2
(a) Classify this equation by:
i. order
ii. linear or nonlinear
iii. separable or nonseparable
(b) Find the general solution of this differential equation. Specify the largest interval I on which the solution is defined.
(c) Verify that your solution is correct by plugging it back into the differential equation.
(d) In part (b), you should have found a one-parameter family of solutions. Find a solution that satisfies the initial condition y(0) = 1.

There are two major tests of readiness for college: the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores in recent years has been roughly normal with mean µ = 20.9 and standard deviation s = 4.8. sat scores are reported on a scale from 400 to 1600. sat scores have been roughly normal with mean µ = 1026 and standard deviation s = 209. reports on a student's act or sat usually give the percentile as well as the actual score. the percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. tanya scores 1260 on the sat. what is her percentile (± 1)?