jofree87 said:dy/dx = (y-x)/(y+x)
I am suppose to solve this equation using substitution, but isn't it possible to solve this equation an easier way since it is an exact equation?
(y+x)dy - (y-x)dx = 0
The differential equation method is a mathematical approach used to model and solve problems involving changing or continuously varying quantities. It is based on the concept of derivatives and involves finding a function that satisfies a given differential equation.
The differential equation method has numerous applications in physics, engineering, economics, biology, and other fields. It is used to model and predict the behavior of systems that involve rates of change, such as population growth, chemical reactions, and electric circuits.
The key steps in solving a differential equation using the differential equation method are: identifying the type of differential equation (e.g. ordinary, partial, linear, non-linear), finding the general solution by integrating the equation, applying initial or boundary conditions to find the particular solution, and verifying the solution by substituting it back into the original equation.
The differential equation method is specifically designed to solve equations that involve derivatives and rates of change. It is different from other methods such as substitution and elimination, which are used to solve algebraic equations. The differential equation method also involves finding a general solution that can be applied to a range of problems, rather than just a single solution.
One of the main challenges of using the differential equation method is that it can be difficult to find an analytical solution for complex equations. In such cases, numerical methods or approximations may be used. Additionally, the method requires a strong understanding of calculus and mathematical concepts, which can be challenging for some individuals.