Solving the Non-Linear ODE: x+ x^2*y+x^3*y^2

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In summary, the speaker is struggling to solve a non-linear ODE encountered in a financial maths course. They are seeking help and have tried various methods without success. Another speaker suggests using a computer to solve it, and the original speaker mentions reading about the linearity of ODEs. They are advised to show their work before determining if they are right or wrong, and someone else suggests using the substitution v=x^2y. It is concluded that while the ODE can be solved analytically, it may be more practical to use numerical methods for computation.
  • #1
scizj
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Hi, All:


I am taking a financial maths course and I encounter the following ODE:

dy/dx = x+ x^2*y+x^3*y^2


I have tried many methods but cannot solve it.

Can anyone help me? Thanks.
 
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  • #3
scizj said:
Hi, All:


I am taking a financial maths course and I encounter the following ODE:

dy/dx = x+ x^2*y+x^3*y^2


I have tried many methods but cannot solve it.

Can anyone help me? Thanks.


The equation is non linear ODE, you probably have to use a computer to solve it for you

have read about linearity of ODEs
 
  • #4
scizj said:
Hi, All:


I am taking a financial maths course and I encounter the following ODE:

dy/dx = x+ x^2*y+x^3*y^2


I have tried many methods but cannot solve it.

Can anyone help me? Thanks.

You will need to show us how and what you did in trying to solve it first before one can ascertain if you're right or wrong.
Hint: Think of letting v= x^2 y.
 
  • #5
I am taking a financial maths course and I encounter the following ODE:
dy/dx = x+ x^2*y+x^3*y^2
I have tried many methods but cannot solve it.
Can anyone help me? Thanks.
This non-linear ODE can be solved, thanks to the general method for solving Riccati equations.
Nevertheless, the analytical solving is rather ardous in the present case : It would involve confluent hypergeometric functions. We could do it, but I am afraid that there would be of no interest for you. Probably, the use of numerical methods of computation would be more convenient in practice.
 

1. Can anyone solve any ODE?

No, not everyone can solve any ODE. Solving ODEs requires a strong mathematical background and knowledge of various techniques and methods. It also depends on the complexity of the ODE and the availability of resources and tools.

2. Do I need to know calculus to solve ODEs?

Yes, a strong understanding of calculus is necessary to solve ODEs. ODEs involve derivatives and integrals, which are fundamental concepts in calculus. It is also helpful to have knowledge of differential equations and linear algebra.

3. Is there a specific method or technique to solve ODEs?

Yes, there are various methods and techniques for solving ODEs such as separation of variables, substitution, and variation of parameters. The choice of method depends on the type and complexity of the ODE.

4. How long does it take to solve an ODE?

The time it takes to solve an ODE depends on its complexity and the method used. Some ODEs can be solved quickly with simple techniques, while others may require more time and effort.

5. Can technology or software be used to solve ODEs?

Yes, technology and software such as Mathematica, MATLAB, and Maple can be used to solve ODEs. These tools have built-in functions and algorithms specifically designed for solving ODEs, making the process more efficient and accurate.

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