- #1
Nikolas7
- 22
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Can you advice the changes in this diff equation:
$\d{y}{x}=\dfrac{y}{x^2+y^2}$
$\d{y}{x}=\dfrac{y}{x^2+y^2}$
Nikolas7 said:Can you advice the changes in this diff equation:
$\d{y}{x}=\dfrac{y}{x^2+y^2}$
This would be wonderful if that was true b/c the equation is homogenous. With the right side numerator of power one, the problem is a little more difficult!Prove It said:I am wondering if this is the correct DE. Are you sure it's not $\displaystyle \begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y^2}{x^2 + y^2} \end{align*}$?
A differential equation is an equation that relates one or more unknown functions to their derivatives. It is used to model various real-world phenomena in fields such as physics, engineering, and economics.
There is no one set method for solving a differential equation, as it depends on the specific equation and its properties. However, some common techniques include separation of variables, using an integrating factor, and using substitution methods.
The notation y/(x^2+y^2) represents a differential equation in the form of dy/dx = f(x,y), where the function f(x,y) is defined as y/(x^2+y^2). This means that the rate of change of y with respect to x is equal to the function y/(x^2+y^2).
The denominator x^2+y^2 represents the distance between the point (x,y) and the origin on a 2-dimensional coordinate plane. This makes the differential equation a type of polar differential equation, where the solution can be interpreted as a curve in polar coordinates.
Yes, differential equations are widely used in various fields to model real-world phenomena such as population growth, chemical reactions, and electrical circuits. They allow for the prediction of future behavior based on current conditions and can also be used to analyze the behavior of systems over time.