anonymous
  • anonymous
x(dy/dx)+y=e^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[x(\frac{ dy }{ dx })+y=e ^{x}\]
anonymous
  • anonymous
what is it you need?
anonymous
  • anonymous
solving for anything?

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anonymous
  • anonymous
it is a linear first order equation coefficient of dy/dx is 1 coefficient of y is 1/x=p R.H.S=q soln is y*integrating factor=integral of (q*integrating factor) w.r.t. x where integrating factor is exp(integral of p w.r.t x)
anonymous
  • anonymous
No integrating factor needed; the equation is ready to be solved as is: \[xy'+y=e^x\\ \frac{d}{dx}\left[xy\right]=e^x\\ xy=\int e^x~dx\\ ~~~~~\vdots\]

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