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# First order ordinary differential equation help please! watch

1. This is the first time ie used integrating factors and I am close to the solution gien..heres my working:

They have:

Where have I gone wrong please?

Thanks
2. 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?
3. (Original post by Chemhistorian)
This is the first time ie used integrating factors and I am close to the solution gien..heres my working:

It is right up to this.
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

They have:

Where have I gone wrong please?

Thanks
4. 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.

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