Class 12

Math

Calculus

Differential Equations

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 coordinate of the point is equal to the x coordinate of the point.

$dxdy y=x$

ydy=xdx

integrating both side

$2y_{2} =2x_{2} +c$

$y_{2}−x_{2}=C$

P(0,-2)

C=-4

$y_{2}−x_{2}+4=0$.