How Do You Find the Equation of a Curve with a Given Slope and Point?

[chakras]

Homework Statement

Find the equation of the curve that passes through the point (1,3) and has a slope of y/x^2 at any point (x,y).

Homework Equations

Is there any general equation for the equation of the curve?

The Attempt at a Solution

the only problem in my homework I am stuck at, do you have to integrate y/x^2? I am quite confused as to how one could get the exact equation of this curve. any help would be appreciated

 

[payumooli]

y' = y/x^2

ODE

solve and sub for constant using codition point (1,3) lies on y=f(x)

 

[HallsofIvy]

y' = y/x^2

ODE

solve and sub for constant using codition point (1,3) lies on y=f(x)

Excellent suggestion.

Of course, this is dy/dx= y/x^2 which can be written as ydy= dx/x^2. Integrate both sides.