# Thread: integrating factor Solve x(dy/dx)=y+x^3

1. ## integrating factor Solve x(dy/dx)=y+x^3

Solve x(dy/dx)=y+x^3

when y=3 and x =1

have i done this correct ?

2. ## Re: integrating factor Solve x(dy/dx)=y+x^3

It all looks good until you say $\displaystyle \displaystyle \int P ~dx = -\frac{1}{x} = \ln x$ which makes little sense.

You are trying to find an integrating factor $\displaystyle \displaystyle I = e^{\int -\frac{1}{x}~dx}$ go from there.

3. ## Re: integrating factor Solve x(dy/dx)=y+x^3

Originally Posted by pickslides
It all looks good until you say $\displaystyle \displaystyle \int P ~dx = -\frac{1}{x} = \ln x$ which makes little sense.

You are trying to find an integrating factor $\displaystyle \displaystyle I = e^{\int -\frac{1}{x}~dx}$ go from there.
As pickslides said, you were good until the middle term of this compound equation: $\displaystyle \displaystyle \int P ~dx = -\frac{1}{x} = \ln x\,.$

It should have been: $\displaystyle \displaystyle \int P ~dx = \int-\frac{1}{x} \,dx= -\ln x\,.$ We ignore the integration constant when finding an integrating factor.

The integrating factor is then: $\displaystyle e^{-ln(x)}\,,$ which can be simplified.