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) .

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

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^(x)dot

Find the equation of the curve whose slope at x=0 is 3 and which passes through the point (0,1) satisfying the differential equation (x^2+1) (d^2y)/dx^2=2x dy/dx .

Find the equation of the tangents to the curve 3x^2-y^2=8 , which passes through the point (4/3,0) .

Find the equation of the normal to the curve 2y=x^2 , which passes through the point (2,1).

The equation of the curve satisfying the differential equation y(x+y^3)dx=x(y^3-x)dy and passing through the point (1,1) is

Find the equation of the normal to the curve x^2=4y which passes through the point (1, 2).

Find the equation of a curve, passes through (-2,3) at which the slope of tangent at any point (x,y) is (2x)/(y^(2)) .

Find the equation of the curve which passes through (1,0) and the slope of whose tangent at (x,y) is (x^2+y^2)/(2xy)