The slope of the tangent to a curve at any point (x,y) on it is given by , where x0 and y0. If the curve passes through the point , find the equation of the curve.

Question

The slope of the tangent to a curve at any point (x,y) on it is given by , where x>0 and y>0. If the curve passes through the point , find the equation of the curve.

Philoid · Accepted Answer

It is given that:

⇒ the given differential equation is a homogenous equation.

The solution of the given differential equation is :

Put y = vx

Integrating both the sides we get:

Resubstituting the value of y = vx we get

the curve passes through the point

⇒ sec

Ans:The equation of the curve is: sec

The slope of the tangent to a curve at any point (x,y) on it is given by , where x>0 and y>0. If the curve passes through the point, find the equation of the curve.