Question: Consider y'+ x 1 y = x 3 . (a) Verify that (x) = x is an integrating factor. (b) Show that when multiplied by

Consider y'+ x−1y = x3.

(a) Verify that α(x) = x is an integrating factor.

(b) Show that when multiplied by α(x), the differential equation can be written (xy)' = x4.

(c) Conclude that xy is an antiderivative of x4 and use this information to find the general solution.

(d) Find the particular solution satisfying y(1) = 0.

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