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

[scizj]

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.

 

[lurflurf]

That is the Riccati equation. It can be reduced by sustituting v=x^3 y.

 

[sozener1]

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

 

[oraclelive]

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.

 

[JJacquelin]

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.