anonymous
  • anonymous
Solve (x-y)dx+xdy=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
y=ux dy=udu+xdx dx=1 so dy=udu+xdx I try to substitute. Is it ok if I leave out the dx?
anonymous
  • anonymous
y=ux dy=udu+xdx dx=1 so dy=udu+x
anonymous
  • anonymous
You have to integrate no?

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anonymous
  • anonymous
do I?
anonymous
  • anonymous
What topic of the course is this from?
anonymous
  • anonymous
homogeneous substitution
myininaya
  • myininaya
i got y=-xlnx+xC
anonymous
  • anonymous
(x-ux)dx+x(udu+x)=0 xdx-uxdx+xudu+x^2=0 work correct so far?
myininaya
  • myininaya
where the C above is a constant
anonymous
  • anonymous
tell me myininaya if my work is correct
myininaya
  • myininaya
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myininaya
  • myininaya
i dont know the way you are doing it im sorry
anonymous
  • anonymous
k. ty.
myininaya
  • myininaya
but i posted above how i got my answer if that helps
anonymous
  • anonymous
please visit site orlandoicc.org
anonymous
  • anonymous
why do you multiply by v?
myininaya
  • myininaya
i multiply by v (i choose this v such that we have vy'+v'y=(yv)')
myininaya
  • myininaya
if we can write the differential equation in this form y'+p(x)y=q(x) then we can multiply by v such that we have vy'+vpy=vq but we want this v so that v'=vp so we can write the next step as (vy)'=vq
myininaya
  • myininaya
v'=pv dv/dx=pv 1/v dv=p dx lnv=p dx so we have v=e^(int p dx)
myininaya
  • myininaya
so we multiply whatever that v is on both sides of the equation then we can write the (vy)'=vq integrate both sides vy=int(vq)+C solve for y y=1/v*int(vq) +C/v

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