find u'(x)

**slapmaxwell1** · February 3rd 2010, 03:26 AM

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..

**CaptainBlack** · February 3rd 2010, 03:58 AM

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 $u(x)$ the left hand side will be the derivative of $u(x)y(x)$ , that is:

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

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

CB

**slapmaxwell1** · February 3rd 2010, 04:12 AM

awesome i actually did it right! wait til my teacher finds out, im not retarded LOL

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