Thank you. But still, it is vague to how to approach the solution analytically.Dr. Courtney said:http://www.wolframalpha.com/input/?i=solve+y'=(3*y^2-x^2)/(2*x-y)++for+y
Not a complete solution, but gives some insight and a way to double check your solution once you have it.
Thank you for your comment. But the problem asks to find a general solution. So, even if it can be approached numerically, do you think this can be considered a general solution?EM_Guy said:Sounds like a problem that requires some kind of numerical method.
Maybe the Newton-Raphson method would work...
http://www.sosmath.com/calculus/diff/der07/der07.html
https://en.wikipedia.org/wiki/Newton's_method
A first order differential equation is a mathematical equation that relates an unknown function to its derivative. It is called "first order" because it contains the first derivative of the unknown function.
A first order differential equation is different from other types of differential equations because it only contains the first derivative of the unknown function, whereas other types may contain higher derivatives. Additionally, first order differential equations do not have specific methods for solving them like linear, exact, or separable equations.
Some common examples of first order differential equations include the logistic equation, the Bernoulli equation, and the exponential growth and decay equation. These equations are often used in fields such as physics, biology, and economics to model real-world phenomena.
Unlike other types of differential equations, there is no specific method for solving first order differential equations. Generally, they are solved by finding an integrating factor or converting the equation into a separable form. In some cases, numerical methods or software may be used to approximate a solution.
First order differential equations have a wide range of applications in various fields such as physics, engineering, economics, and biology. They are used to model population growth, chemical reactions, electrical circuits, and many other natural phenomena. They are also essential in understanding and predicting the behavior of complex systems.