How Can You Solve a Non-Exact Differential Equation?

In summary, the conversation is about a tough differential equation that the speaker is struggling to solve. They have tried various techniques but have not been successful. They also mention using Maple but it was unable to solve it. The speaker is supposed to know how to solve this type of equation based on their previous exam question.
  • #1
Feynmanfan
129
0
Tough differential equation

Hello!

I'm having real trouble with this differential equation. I don't want you to solve it for me. Just give me a hint what I should do.

(1+7x+6y+3x^2+4xy+5y^2)dx+2(1+2x+5y)dy=0

Obviously it is not exact. But I'm trying to find an integrating factor..
May be I should use another technique.
 
Last edited:
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  • #2
It's a tough one isn't it?
 
  • #3
I think it has no simple solution. Maple gave up after a while...
 
  • #4
well, I am suposed to know how to solve it. THat was last year's exam question!
 
  • #5
Do u at least know what u were supposed to to be doing??I mean the theory behind (non)exact ODE??

Daniel.
 
  • #6
I don't understand your question. I've been trying all techniques I learned (homogeneous, isobaric equation, exact equations, integrating factor,...). But I can't solve it.
 

1. How can I determine the complexity of a differential equation?

The complexity of a differential equation can be determined by looking at the order, degree, and linearity of the equation. The order refers to the highest derivative present, the degree refers to the highest power of the derivative, and linearity refers to whether the equation is linear or nonlinear.

2. What is the best approach for solving a tough differential equation?

The best approach for solving a tough differential equation is to first try to separate variables, if possible. If not, then using an appropriate substitution or change of variables can help simplify the equation. If these methods do not work, then using numerical methods or computer software may be necessary.

3. How can I check if my solution to a differential equation is correct?

You can check if your solution to a differential equation is correct by plugging it back into the original equation and verifying that it satisfies the equation. You can also use software or online tools to graph both the original equation and your solution to visually check for accuracy.

4. What are some common mistakes to avoid when solving a tough differential equation?

Some common mistakes to avoid when solving a tough differential equation include: not properly understanding the problem, making careless algebraic errors, not simplifying the equation enough before attempting to solve it, and not checking the solution for correctness.

5. How can I improve my skills in mastering tough differential equations?

To improve your skills in mastering tough differential equations, it is important to practice solving a variety of problems. It can also be helpful to review the fundamentals of differential equations, such as different methods for solving different types of equations. Additionally, seeking guidance from a mentor or taking a course on differential equations can also aid in improving skills.

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