Question 2

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation. (i) xy = a ex + b e- x + x2 : 2/2 2 2 2 0d y dyx xy x dxdx + − + − = (ii) y = ex (a cos x + b sin x) : 2 2 2 0d y dy ydxdx − + = (iii) y = x sin 3x : 2 9 6cos3 0d y y x dx + − = (iv) x2 = 2y2 log y : 2 2( ) 0 dyx y xy dx+ − =