MATH 202 Exam 2, Spring 2015

ie f , ; b. Use the substitution x =e to change the given differential equation x*y"+5xy'+4y =34+(ln x)? x to a differential equation with constant coefficients. THEN STOP! = (To get full credit, you must prove the necessary Chain Rule formulas) X= a. —) b> \nx ——) 4 = EU) L= P(x) ot. c! a _@ Problem 3 roo“ Find the general solution 0 substitution. Problem 1, E Justify your answer carefully. b. Suppose that P(x), q(x), r(x)and ia (x) are continuous everywhere. Is it possible thar = 2. y = ot ey = 2 are all solutions of the differential equation y+ p(x)y” + q(x)y' + r(x)y Ef (x) Justify your answer carefully. | (Hint: The three given functions have the property that y(0)=2) y Answer part (a) OR part (b). — ee : 2 Problem 2. [0 a. Find the right form of a particular solution yy Of the differential equation. me y4) +2y"+y=A4xsinx +e (DO NOT SOLVE for the constants/coefficients). ae yo tay! y= a) ie f , ; b. Use the substitution x =e to change the given differential equation x*y"+5xy'+4y =34+(ln x)? x to a differential equation with constant coefficients. THEN STOP! = (To get full credit, you must prove the necessary Chain Rule formulas) X= a. —) b> \nx ——) 4 = EU) L= P(x) ot. c! a _@ Problem 3 roo“ Find the general solution 0 substitution. on using the method of