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8. Let's see if we can better clarify the process used to solve these linear differential equations. a] Rewrite the standard form of a linear differential equation shown on the previous page. lf'h'lultipl},lr both sides of the equation by Hz). b] Express .f{17:l in terms of POE) in such a way that the left side of the differential equation always forms the result of a product rule. C] Use this to solve the initial value problem. d? U dx+1+x_x(1+x) y 1 d] Demonstrate that this integrating factor did indeed do its job. Diiferentiate I (15)}? with respect to x by performing the product rule. Did you get what you are supposed to get? e] Check your work by substituting your solution in for j; in the original differential equation. 9. Solve the differential equation. div + ii] = 5 x as: 3' 1i]. Solve the initial value problem. :13; Exy _ E+I+x2=5mx y(D)=3