anonymous
  • anonymous
Solve the differential equation. xy' - (x + 1)y = 0
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
x(dy/dx) - (x+1)y = 0 x(dy/dx) = (x+1)y dy/dx = [ (x+1)/x ] y 1/y (dy) = (x+1)/x dx ::: integrate can yu go from there?
anonymous
  • anonymous
somehow i got (x-1)/x
anonymous
  • anonymous
as a final answeR?

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anonymous
  • anonymous
noo instead of (x+1)/x dx
anonymous
  • anonymous
my final answer was y = -1/2Ce^x(x)^-2
anonymous
  • anonymous
i have a feeling that's not right
anonymous
  • anonymous
hmm not what i got, wait i'm gonna type what i have
anonymous
  • anonymous
ok now i'm up to ln(y) = x + ln(x) + C.. not sure what to do next
anonymous
  • anonymous
\[xy' - (x + 1)y = 0\]\[x{dy \over dx} - (x+1)y = 0\]\[x{dy \over dx} = (x+1)y\]\[{dy \over dx} = {(x+1) \over x} (y)\]\[{1 \over y} dy = {(x+1) \over x} dx\] Integrate:\[\ln|y|= \ln|x|+x +C\]\[e^{lny} = e^{lnx+x+C}=e^{lnx}*e^{x}*e^{C}\]\[y = A*x*e^{x}\] \[y = Axe^{x}\] that's what i have
anonymous
  • anonymous
is that right?
anonymous
  • anonymous
I think soo.. what is A?
anonymous
  • anonymous
e^C = constant a constant which i called A, you can called it whatever..
anonymous
  • anonymous
but did yu understand everything?
anonymous
  • anonymous
ohh gotcha.. i understand it.. thank you.. can you help me with other problems too?
anonymous
  • anonymous
good. i sure can, just post them and i'll try
anonymous
  • anonymous
\[\int\limits_{1/2}^{2} \] [(e^1/x) / (x^2)] dx
anonymous
  • anonymous
\[\int\limits_{2}^{2}{{e^{1} \over x} \over x^{2}} dx\] is that what yu tried to write
anonymous
  • anonymous
\[{e^{1/x} \over x^{2}}\]
anonymous
  • anonymous
that didn't come out on my computer - maybe bc i'm using a mac. but its the integration bounded from 1/2 to 2
anonymous
  • anonymous
and the function that you just wrote
anonymous
  • anonymous
ok
anonymous
  • anonymous
do a product rule between e^(1/x) and x^(-2)
anonymous
  • anonymous
can you do that ?
anonymous
  • anonymous
i'm not really sure.. the integration of e^(1/x) is just e^(1/x)?
anonymous
  • anonymous
-e^(1/x)*x^-1??
anonymous
  • anonymous
the final answer comes up to be e^2 - sqrt(e) i think
anonymous
  • anonymous
how did you get that?

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