The slope of the tangent any point on a curve is `lambda` times the slope of the joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

Explanation

Let `P(x,y)` be any point on the given curve.

The slope of the tangent at point `P=λ` (Slope of the line joining the point `P` and the origin)

So, `frac{dy}{dx}=lambda (frac{y-0}{x-0})=>frac{dy}{dx}=lambda frac{dx}{x}`

This is required differential equation,
On integrating and we get,

`int dy/y=lambda int dx/x`
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