The solution of the differential equation `xdx+ydy =(xdy-ydx)/(x^(2)+y^(2))` is `tan(f(x, y)-C)=(y)/(x)` (where, C is an arbitrary constant). If `f(1, 1)=1`, then `f(pi, pi)` is equal to

The solution of the differential equation xdx+ydy+(xdy-ydx)/(x^(2)+y^(2))=0 , is

The solution of differential equation xdx+ydy=a(x^(2)+y^(2))dy is

Solution of the differential equation (xdy)/(x^(2)+y^(2))=((y)/(x^(2)+y^(2))-1)dx , is

The solution of the differential equation (dy)/(dx)=(xy+y)/(xy+x) is y-lambda x=ln((x)/(y))+C (where, C is an arbitrary constant and x, y gt0 ). Then, the valeu of lambda is equal to

xdx+ydy+[xdy-ydx]/[x^2+y^2]=0

If the solution of the differential equation (1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0 is x+kye^((x)/(y))=C (where, C is an arbitrary constant), then the value of k is equal to

The solution of the differential equation xdy=(tan y+(e^(1)//x^(2))/(x)secy)dx is (where C is the constant of integration)

The solution of differential equation xdy(y^(2)e^(xy)+e^(x//y))=ydx(e^(x//y)-y^(2)e^(xy)), is

The solution of the differential equation xdy-ydx+3x^(2)y^(2)e^(x^(3))dx=0 is (where, c is an arbitrary constant)

The general solution of the differential equation (dy)/(dx)=2y tan x+tan^(2)x, AA x in (0, (pi)/(2)) is yf(x)=(x)/(2)-(sin(2x))/(4)+C , (where, C is an arbitrary constant). If f((pi)/(4))=(1)/(2) , then the value of f((pi)/(3)) is equal to