Find the particular solution of the differential equation `(dy)/(dx)+ycotx=2x+x^2cotx(x!=0)`given that `y = 0`when `x=pi/2`.

Find the particular solution of the differential equation `(dy)/(dx)+y

1.	Find the particular solution of the differential equation `(dy)/(dx)+ycotx=2x+x^2cotx(x!=0)`given that `y = 0`when `x=pi/2`.
Answer» Correct Answer - `y = x ^(2) +C cosec x ` `IF = e ^(int cot x dx ) = e ^(log sinx ) = sinx ` `yxx sinx = int (x ^(2) cot x + 2x) sinx dx + C ` ` " "= int x ^(2) cos x dx + int 2 x sinx dx +C` `= x ^(2) sinx - int 2x sin x dx + int 2x sinx dx +C = x ^(2) sin x +C `