First order ordinary differential equation help please! Watch
- Thread Starter
- 24-03-2011 10:48
- 24-03-2011 10:56
It's all correct until you started integrating - you can't take out variables from the integrals like that. The idea of the integrating factor is that you can get it into a form where you can integrate it by inspection, since it is in the form v du/dx + u dv/dx, which is the product rule for differentiation. If you compare x³ dy/dx + 3x²y with that form, can you see what it must integrate to?
(Original post by Chemhistorian)
- 24-03-2011 16:04
This is the first time ie used integrating factors and I am close to the solution gien..heres my working:
You can not integrate pointwise, but now you can write the equation as
using the product rule for differentiation.
This form is why you use integration factor, I think.
(the equation may be solved another ways, too).
Multiplying by dx you get differential of
and integrating this gives the solution
Last edited by ztibor; 24-03-2011 at 16:12.
- 24-03-2011 17:13
Just to add to that - the integrating factor method is obtained from the assumption that the left hand side can be written as a derivative of a product, and from this assumption the factor e^integral of P dx is obtained. Because of that, whenever you multiply a first order ordinary differential equation by the integrating factor, the left hand side will always be in the form of a derivative of a product.