- #1
gvk
- 83
- 0
Very simple in writing, but hard to solve:
[tex] x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)[/tex]
:tongue2:
[tex] x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)[/tex]
:tongue2:
Maybe convert to polar coodinates? That x2+y2 wants to be r2. Maybe not thoughgvk said:Very simple in writing, but hard to solve:
[tex] x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)[/tex]
:tongue2:
gvk said:Very simple in writing, but hard to solve:
[tex] x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)[/tex]
:tongue2:
An ODE (Ordinary Differential Equation) is a mathematical equation that describes how a variable changes over time. It involves one or more derivatives of a dependent variable with respect to one or more independent variables.
ODEs are important in many fields of science and engineering because they can be used to model and predict the behavior of systems over time. They are particularly useful in areas such as physics, chemistry, biology, and economics.
The process of solving an ODE involves finding a function that satisfies the equation. This can be done analytically, using mathematical techniques such as separation of variables or integration, or numerically using computational methods.
ODEs are used in a wide range of applications, including predicting the motion of celestial bodies, modeling population growth, analyzing chemical reactions, and forecasting economic trends.
An ODE can be considered interesting if it has complex solutions, involves a unique or novel application, or has significant implications for understanding a particular phenomenon. Additionally, ODEs that have connections to other areas of mathematics or have practical applications can also be considered interesting.