If the curve satisfying `ydx+(x+x^2y)dy=0` passes through `(1,1)` then `((-4log_3(4)+1/(y(4)))/2)` is equal to

The curve satisfying ydx-xdy+ln xdx=0,(x>0) passing through (1,-1) is

If the curve satisfying (xy^(4) + y)dx - xdy = 0 passes through (1,1) then the value -41(y(2))^(3) is _______

If the curve satisfying (xy^(4) + y)dx - xdy = 0 passes through (1,1) then the value -41(y(2))^(3) is _______

The curve satisfying (d^(2)y)/(dx^(2))-4y'=0 and passing through (1,0) is

The curve satisfying (d^(2)y)/(dx^(2))-4y'=0 and passing through (1,0) is

If the curve satisfying (1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0 passes through (1,1) then 9+y(2)e^((2)/(y(2)))-e is equal to-