Let `y=y(x)` be the equation of a curve whose slope at `(x,y)` is `-((x+y))/(x)` and which passes through the point `(2,1)`.Then value of `y(1)` is

Prove that the equation of a curve whose slope at (x,y) is -(x+y)/x and which passes through the point (2,1) is x^2+2xy=8

Find the equation of the curve whose gradient at (x,y) is y/(2x) and which passes through the point (a,2a) .

Show that the equation of the curve whose slope at any point is equal to y+2x and which passes through the origin is y+2(x+1)=2e^(2x)

show that the equation of the curve whose slope at any point is equal to y+2x and which passes through the origin is y+2(x+1)=2e^(2x)

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^(x) - x-1) .

The equation of the curve whose slope is given by (dy)/(dx)=(2y)/(x);x>0,y>0 and which passes through the point (1,1) is x^(2)=yby^(2)=x c.x^(2)=2y d.y^(2)=2x

The equation of the curve,slope of whose tangent at any point (h,k) is (2k)/(h) and which passes through the point (1,1) is (i)x^(2)=y( ii) y^(2)=x( iii) x^(2)=2y( iv )y^(2)=2x