Find the particular solution of the differential equation `(1+x^2)(dy)/(dx)+2xy=1/(1+x^2)` given that `y=0` when `x=1`

Find the particular solution of the differential equation (1+x^2)(dy)/(dx)+2xy=1/(1+x^2) ,when y=0 , x=1 .

Find the particular solution of the differential equation (1 - x ^(2) ) (dy)/(dx) - xy = x ^(2) , given that y = 2 when x = 0 .

Find the particular solution of the differential equation (1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2)) given that at x=1 , y=0 .

Find the particular solution of the differential equation (1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2)) given that at x=1 , y=0 .

Find the particular solution of the differential equation x(dy)/(dx) - y = (x + 1 ) e^(-x) given that y = 0 when x = 1 .

Find the particular solution of the differential equation x(x^(2)-1)(dy)/(dx) =1, it being given that y = 0 when x = 2.

Find the particular solution of the differential equation (dy)/(dx) = 2xy^(2) given that y = 1, when x = 0.