Solving ODE Problem: Tips and Techniques for Postgrad Students

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In summary, an ODE (ordinary differential equation) problem is a mathematical problem that involves finding a function that satisfies a given differential equation. Solving these problems is important for postgraduate students in many scientific fields, and some tips for solving them include carefully reviewing the problem, using appropriate techniques, and checking for accuracy. Common techniques used to solve ODE problems include separation of variables, substitution, integrating factors, and power series solutions. To improve skills in solving ODE problems, one can practice regularly, seek help from resources, and stay organized.
  • #1
dec46
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Hi All,

I am a postgrad student looking for help in solving this ODE.


Homework Statement



[tex]\frac{dy}{dx}[/tex]=[tex]\frac{y^{2}+xy^{2}}{x^{2}y-x}[/tex]


Homework Equations





The Attempt at a Solution


I have been attempting to solve this by substitution but without success, any help would be appreciated.

 
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  • #2
It looks separable.
 
  • #3
The furthest I can get is

[tex]x(xy-1)dy=(x+1)y^{2}dx[/tex]

but do not know where to go from here?
 

FAQ: Solving ODE Problem: Tips and Techniques for Postgrad Students

What is an ODE problem?

An ODE (ordinary differential equation) problem is a mathematical problem that involves finding a function that satisfies a given differential equation. These equations describe how a quantity changes over time, and solving them involves finding the relationship between the unknown function and its derivatives.

Why is solving ODE problems important for postgraduate students?

Solving ODE problems is important for postgraduate students because it is a fundamental skill in many scientific fields, including physics, engineering, and mathematics. It allows for the modeling and analysis of complex systems and phenomena, and is often used in research and practical applications.

What are some tips for solving ODE problems?

Some tips for solving ODE problems include carefully reviewing the problem and identifying the type of equation, using appropriate techniques and methods for the specific type of equation, and checking your solution for accuracy and consistency. It can also be helpful to break the problem down into smaller steps and to practice solving similar problems.

What are some common techniques used to solve ODE problems?

Some common techniques used to solve ODE problems include separation of variables, substitution, integrating factors, and power series solutions. These techniques involve manipulating the given equation to make it easier to solve, and may require knowledge of basic calculus and algebra.

How can I improve my skills in solving ODE problems?

To improve your skills in solving ODE problems, it is important to practice regularly and seek help from resources such as textbooks, online tutorials, and professors or tutors. It can also be helpful to work on problems with a study group or to attend workshops or seminars on ODE problem-solving techniques. Additionally, staying organized and taking good notes can aid in understanding and solving these problems.

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