Question

Find the equation of a curve passing through the point (0,-2) given that at any point (x, y)on the curve the product of the slope of its tangent and y co-ordinate of the point is equal to the x co-ordinate of the point.

Answer 1

$\frac{dy}{dx}y=x$

$\Rightarrow ydy=xdx\Rightarrow y^2=x^2+c--\left(1\right)(0,-2)lieson\left(1\right)\Rightarrow 4=c\Rightarrow y^2=x^2+4$