Why Is This First Order Non Linear Differential Equation So Challenging?

In summary, the given equation is not exact, homogeneous, or separable. The common factor of y^2 was eliminated, but the problem still remains unsolved. Further assistance is needed.
  • #1
Darkestsolrac
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Homework Statement



(8x^2y^3-2y^4)dx+(5x^3y^2-8xy^3)dy=0

Homework Equations


The Attempt at a Solution



I've already tried the most logical steps. The equation isn't exact and I couldn't find an integrating factor to make it exact. It's also not homogeneous or separable. I have to be making an error somewhere. I've done all my other questions but this one is just killing me. Help please!
 
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  • #2
(8x^2y^3-2y^4)dx+(5x^3y^2-8xy^3)dy=0
...
I've already tried the most logical steps.
Did you get rid of the common factor of y^2 :$$\frac{dy}{dx}=\frac{2y^2-8x^2y}{5x^3-8xy}$$
... where does this come from?
 

FAQ: Why Is This First Order Non Linear Differential Equation So Challenging?

What is a first order non linear differential equation?

A first order non linear differential equation is a mathematical equation that relates a function with its derivative, where the function and/or its derivative are non linear. This means that the equation cannot be solved by standard methods, and may require numerical or approximate solutions.

Can you give an example of a first order non linear differential equation?

One example of a first order non linear differential equation is the logistic differential equation, which describes the growth of a population over time and is given by dy/dt = ky(1-y), where k is a constant.

What is the difference between a linear and a non linear differential equation?

A linear differential equation is one where the function and its derivative are both linear, meaning they can be expressed as a sum of constant coefficients and variables. A non linear differential equation, on the other hand, cannot be expressed in this way and may include higher powers or products of variables and their derivatives.

How do you solve a first order non linear differential equation?

Solving a first order non linear differential equation can be a complex process and may require numerical or approximate methods. Some common techniques include separation of variables, substitution, and using power series or numerical methods.

Why are first order non linear differential equations important in science?

First order non linear differential equations are important in science because they can model a wide range of physical phenomena, from population growth to chemical reactions to electrical circuits. They also often arise in real-world situations and can provide insight into complex systems and processes.

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