VARIABLE SEPARABLE Determine the solution of the following differential equations. Choose the correct answer by shading the circle corresponding to your choice. Show your detailed solutions. 1. (x2 -9)dy - xydx = 0 o y = c(x -9) o y' = c(x - 9) o yz = c(x2 -9) o x = c(yz+9) 2. e-3x-1 Inydy - ye* dx = 0 0 2(Iny)2 - e4x+1 = c o Iny2 - e4x+1 = c o Iny? + et* = c o 2(Iny)2 - ex = c 3. sin 2q tan? B do + (sec2 8 - 1) cos q dB = 0 o B = 2 sing + c ( = 2 sec B + c o q = 2tan B + c o B = 2coso + c 4. tan x dy + y'sin x dx = 0, when x = 0, y = 1 o y(3 - cos 2x) = 2 o y2 (2 - cos 2x) = 1 o y(cos 2x - 2x) = 1 o y(cos 2x - 1) = x 5. ey-2x(1 + x2 )dx + cosy dy = 0, when x = 0, y = 0 O 2e *(cosy - sin y) + e(2x2 + 2x + 3) = 5e2x+y o 2e (cosy - siny) + ex(2x2 + 2x + 3) = 5ey-2x ezx (siny - cosy) + 2ey(2x2 - 2x - 3) = 5e2x+y O e?*(cosy - sin y) + 2e"(2x2 + 2x + 3) = 5ey-2x