Let `y=f(x)` satisfies the equation `dx+ dy +e^3(x^2+2xy+y^2)dx=0` with `f(1)=1/e-1.` Identify which of the following statement(s) is(are) correct?

Let y=f(x) be satisfying differential equation e^(-x^(2))(dy)/(dx)=2xy^(2) such that f(0)=(1)/(2) Which of the following statements is correct about f(x) ?

Let y=f(x) be satisfying differential equation e^(-x^(2))(dy)/(dx)=2xy^(2) such that f(0)=(1)/(2) Q. Which of the following statement is correct about f(x) ?

If y=f(x) satisfy differential equation ( dy )/(dx)-y=e^(x) with f(0)=1 then value of f'(0) is

y = f(x) which has differential equation y(2xy + e^(x)) dx - e^(x) dy = 0 passing through the point (0,1). Then which of the following is/are true about the function?

y = f(x) which has differential equation y(2xy + e^(x)) dx - e^(x) dy = 0 passing through the point (0,n 1). Then which of the following is/are true about the function?

Let y=f(x) satisfy the differential equation (dy)/(dx)=(x+y)/(x),y(1)=1, then y((1)/(e)) is equal

Let y=f(x) be function satisfying the differential equation (y^(2)x-y^(2))dx-xydy-0 and y(1)=e then the range of the function f(x) is: