If `y` satisfies `(dy)/(dx)=(e^(y))/(x^(2))-(1)/(x)` and `y(1)=0` then the value of `e^(y(2))` is

Let y=f(x) satisfies (dy)/(dx)=(x+y)/(x) and f(e)=e then the value of f(1) is

Solve : (dy)/(dx)=e^(x+y)+x^(2)e^(y)

If y=e^((5)/(x))(2x^(2)-1)^((1)/(2)) then the value of ((dy)/(dx))/(y) is

Solve (dy)/(dx)=e^(x-y)+x^(2)e^(-y) .

If xsin((y)/(x))dy = (y sin((y)/(x))-x)dx and y(1) = (pi)/(2) then the value of cos((y)/(e^(7))) is __________.

Solve: (dy)/(dx)=e^(x-y)+x^2e^(-y)

If (dy)/(dx)=e^(-2y) and y=0 when x=5, then the value of x for y=3 is

If K is constant such that xy + k = e ^(((x-1)^2)/(2)) satisfies the differential equation x . ( dy )/( dx) = (( x^2 - x-1) y+ (x-1) and y (1) =0 then find the value of K .

If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =