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.
A differential equation is a mathematical equation that involves an unknown function and its derivatives. It describes how a quantity changes over time or in relation to other variables.
The solution to a differential equation is a function that satisfies the equation when its derivatives are substituted into the equation. It represents the relationship between the variables described by the equation.
Differential equations are used to model real-world phenomena in many fields, including physics, engineering, and economics. Understanding them allows us to make predictions and solve problems in these areas.
The method for solving a differential equation depends on its type and complexity. Some can be solved analytically using mathematical techniques, while others require numerical methods or computer simulations.
This means that the mathematical solution has been found, but the significance or implications of the solution are not fully understood. Further analysis and interpretation may be needed to fully grasp the meaning of the solution in the context of the problem being studied.