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) .

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

What is the equation of the curve whose slope any point is equal to 2x and which passes through the origin?

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) .