Differential equation given integrating factor

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Homework Statement



Show that given function μ is an integrating factor and solve the differential equation..

y^2 dx + (1 + xy) dy = 0 ; μ(x) = e^xy



The Attempt at a Solution



let M = y^2
N = (1 + xy)

dM/dy = 2y dN/dx = y hence, not exact equation.

times μ(x) = e^xy to the not exact equations...

2y(e^xy) dx + y(e^xy) dy = 0

let M = 2y(e^xy)
N = y(e^xy)

dM/dy = 2(e^xy) + 2y(e^y) ---> apply product rule

dN/dx = 0(e^xy) + y(e^y) ---> apply product rule

the problem is.. the equations still not the exact equations..
How to proceed?
 

Answers and Replies

  • #2
HallsofIvy
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Yes- which means that [itex]\mu= e^{xy}[/itex] is NOT an integrating factor. Something is wrong with that question.
 
  • #3
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Yes- which means that [itex]\mu= e^{xy}[/itex] is NOT an integrating factor. Something is wrong with that question.
So... i can't solve this equation? the equation doesn't have any solutions?
 

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