Can’t get a start on solving a first order differential equation

In summary, the conversation is discussing how to solve a first order, non-linear differential equation. The equation is given along with parameters, and the goal is to find a general solution and a constant. The individual has attempted to solve using separation of variables and testing for exactness, but has not been successful. They have also tried using integrating factors, but are unable to get a function of x or y alone. They are seeking guidance on how to approach the problem.
  • #1
ifly2hi
5
0

Homework Statement


Am looking at a first order, non linear differential equation. I want to solve for a general solution and will have to find a constant with given parameters. Equation: 3x2y+8xy2+[itex]([/itex]x3+8x2y+12y2[itex])[/itex][itex]dy/dx[/itex]=0 Parameters: y(2)=1

Homework Equations


[itex]∂M/∂y[/itex]=[itex]∂N/∂x[/itex] (Exactness) & [itex](My-Nx)/N[/itex] (integrating factors)

The Attempt at a Solution


I have tried to use separation of variable with no avail. When I try to separate them I can’t get it into terms of just x or just terms of y. I have tested for exactness and it failed, so I moved to the next step of integrating factors. After trying to solve for integrating factors I still cannot get function of x alone or y alone. When solveing for the equation listed in “Relevant equations” I get:((6xy+8y2-(24y+8x2))/(3x2y+8xy2).

Have tried intergrating factors both ways and still can't get a function of x or y alone. Can someone point in the right direction to starting this problem. I am swinging the bat but missing the ball b/c I don't see it. Thank you
 
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  • #2
You must have computed [itex]M_{y}[/itex] and/or [itex]N_{x}[/itex] incorrectly, because they are equal.
 
Last edited:
  • #3

Homework Statement


Am looking at a first order, non linear differential equation. I want to solve for a general solution and will have to find a constant with given parameters. Equation: 3x2y+8xy2+[itex]([/itex]x3+8x2y+12y2[itex])[/itex][itex]dy/dx[/itex]=0 Parameters: y(2)=1

Homework Equations


[itex]∂M/∂y[/itex]=[itex]∂N/∂x[/itex] (Exactness) & [itex](My-Nx)/N[/itex] (integrating factors)

The Attempt at a Solution


I have tried to use separation of variable with no avail. When I try to separate them I can’t get it into terms of just x or just terms of y. I have tested for exactness and it failed, so I moved to the next step of integrating factors. After trying to solve for integrating factors I still cannot get function of x alone or y alone. When solveing for the equation listed in “Relevant equations” I get:((6xy+8y2-(24y+8x2))/(3x2y+8xy2).
6xy+ 8y is My but 24y+ 8x2 is Ny, not Nx.

Have tried intergrating factors both ways and still can't get a function of x or y alone. Can someone point in the right direction to starting this problem. I am swinging the bat but missing the ball b/c I don't see it. Thank you
 

1. How do I begin solving a first order differential equation?

The first step in solving a first order differential equation is to identify the type of equation you are dealing with. Is it separable, linear, exact, or inhomogeneous? Once you know the type of equation, you can use the appropriate method to solve it.

2. What are the different methods for solving first order differential equations?

There are several methods for solving first order differential equations, including separation of variables, integrating factors, and substitution. It is important to choose the method that best fits the type of equation you are solving.

3. Can I use a calculator to solve a first order differential equation?

Yes, you can use a calculator to solve a first order differential equation. However, it is important to have a good understanding of the underlying concepts and methods before relying on a calculator. Additionally, some calculators may not have the necessary functions to solve more complex equations.

4. What are the initial conditions in a first order differential equation?

The initial conditions in a first order differential equation refer to the starting values of the dependent and independent variables. These conditions are typically given in the problem and are used to find the particular solution to the equation.

5. How can I check if my solution to a first order differential equation is correct?

To check if your solution to a first order differential equation is correct, you can plug it back into the original equation and see if it satisfies the equation. Additionally, you can use a graphing calculator to plot both the original differential equation and your solution to visually compare them.

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