# find u'(x)

• Feb 3rd 2010, 03:26 AM
slapmaxwell1
find u'(x)
so i have the function: Y^'+ P(x)y=Q(x) where u(x) is the integrating factor, find u'(x).

i have an answer i wanted to know if its right? i dont know why but i can attach my pdf file, anyways my answer is u'(x) = P(x)u(x)....is this right? thanks in advance..
• Feb 3rd 2010, 03:58 AM
CaptainBlack
Quote:

Originally Posted by slapmaxwell1
so i have the function: Y^'+ P(x)y=Q(x) where u(x) is the integrating factor, find u'(x).

i have an answer i wanted to know if its right? i dont know why but i can attach my pdf file, anyways my answer is u'(x) = P(x)u(x)....is this right? thanks in advance..

When you multiply through by $\displaystyle u(x)$ the left hand side will be the derivative of $\displaystyle u(x)y(x)$, that is:

$\displaystyle \frac{d}{dx}\left[u(x)y(x)\right]$ $\displaystyle = u(x)y'(x)+u'(x)y(x)= u(x)y'(x)+u(u)P(x)y(x)=u(x)Q(x)$

So $\displaystyle u'(x)=P(x)u(x)$

CB
• Feb 3rd 2010, 04:12 AM
slapmaxwell1
awesome i actually did it right! wait til my teacher finds out, im not retarded LOL