CHEM 110 Midterm: CHEM 110 NIU CHEM110 Practice Exam 1
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Determine the solution y(x) of the initial value problem xy = x+4y, y(1) = 2: (18 pts. ) Find the solution y(x) of the initial value problem (4x + 1)y = y3, y(0) = 2: (18 pts. ) Find the general solution y(x) of xy2 dy dx. Find the general solution of (cid:16)cos 2x + y 2 + 2x 2 ln y(cid:17) + (cid:16)y 1 2x 1y 1 2xy 3(cid:17) dy dx. Use the method of undetermined coe cients to nd the general solution y(x) of y 3y + 2y = 2ex + e3x: (10 pts. ) Determine the form of the particular solution yp(x) of the following di erential equation. (do not solve for the unknown coe cients. ) y(3) + 4y = x2ex + x + cos 2x: (10 pts. ) Use the improved euler method with step size h = 1/2 to approximate y(2), where y(x) is the solution of the initial-value problem dy dx.
