A curve passes through the point (3, -4) and the slope of . the is the tangent to the curve at any point (x, y) is `(-x/y)` .find the equation of the curve.

Find the equation of the curve passing through the point (1,0) if the slope of the tangent to the curve at any point (x,y)is(y-1)/(x^(2)+x)

The slope of the tangent to the curve at any point is equal to y + 2x. Find the equation of the curve passing through the origin .

Find the equation of a curve passing through the point (0,1) .If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of the coordinates of the point.

A curve passes through the point (2,-8) and the slope of tangent at any point (x,y) is given by x^(2)/2-6x . The maximum ordinate on the curve is given by lambda then find (3lambda ).

A curve passes through the point (1,(pi)/(6)). Let the slope of the curve at each point (x,y) be (y)/(x)+sec((y)/(x)),x>0. Then the equation of the curve is

A curve passes through the point (1,(pi)/(6)). Let the slope of the curve at each point (x,y) be (y)/(x)+sec((y)/(x)),xgt0. Then, the equation of the curve is

Let us consider a curve, y=f(x) passing through the point (-2,2) and the slope of the tangent to the curve at any point (x,f(x)) is given by f(x)+xf'(x)=x^(2) . Then :