The problem involves a function y = g(x) and requires writing a differential equation of the form "dy/dx = f(x,y)" such that g is one of its solutions. The context includes a tangent line to the graph of g that intersects the x-axis at a specific point.
Some participants have provided insights into expressing the slope of the tangent line, while others are seeking clarification on the reasoning behind the proposed differential equation. There appears to be ongoing exploration of the problem without a definitive consensus.
Participants note the challenge of understanding both the reasoning and the methodology behind deriving the differential equation from the given conditions.
negatifzeo said:Homework Statement
In this problem, a function y= g(x) is described. Write a differential equation of the form "dy/dx=f(x,y) having the function g as it's solution (or one of it's solutions).
The line tangent to the graph of g at the point (x,y) intersects the x-axis at the point (x/2,0).
Homework Equations
The Attempt at a Solution
The solution is y'=2y/x. I'm having trouble seeing both why and how.