answer this give complete solution problem 1 to 5 and write in paper or notebook, the answer already given. The topic is separation of variables

= ) log (sing) = log ( c cos xx ) = ) sing = ccost. where c is the constant. 3. 2cyd " dy = 0 = xy dx = _ ex -dy = ) ace dx = -y dy integrating both sides we get, Socedr =-Syldy how using the desult, Sxe "'dxs - Le Le and Syfy = 4-2 we get -p - x 2 2 + c' =4 40 - * 2 = C where C = - C' is the constant. 4. Zyd x = 3x dy =) 2dx - 3dy y integrating both sides we get 2 fax = 3 fat = ) 2 loglal = 3 log141 + logclog x2= logy + logc - ) x 2 = cy3 where C is the constant. 5. mydoc= hedy = max = hoy integrating bothsides x y 2 =] m logx = h logy + loge = am cyn where Cis the constant1. Given that (1-x ) y = y= =) ( 1-x ) dy 42 dx - dy - doc = y dy = dx 1 - 2 1 - XC integrating both sides we get Syaly = [,de using Syndy = yotl dx and = loglax+bl) h+1 axtb a we get - 1 = log (1- 341 ) - = Dog ( CILx) - # log ( = ) - - 1 = ) y log ( c/1- x1) = 1. where ais the constant. 2. Sinx Sing dx + cosxcosydy = 0 = ] Sinx singdx = - cosx cosy cly COST =) Sink ex = - COL dy Now integrating both sides sing we get ? Sthx cosx (cosy dy sing using the sesult ( sink by - - log (cost) and casx sing we get - log ( cost ) = - log ( sincy) ) + lose