nubeer
  • nubeer
Calc 3... how do we find the integration factor of equation which is not exact.. (i want to know for in which both x and y is used as integration factor)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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UnkleRhaukus
  • UnkleRhaukus
do you have an example we can work through /
nubeer
  • nubeer
hmm no i don't have any example .. we were asked to look for it.. i just want to know any general method.. any link or inofrmation would appreciate it.. its basically part of diffrential equations.
UnkleRhaukus
  • UnkleRhaukus
\[\left(3x+\frac 6y\right)\text dx+\left(\frac {x^2}{y}+\frac{3y}{x}\right)\text dy =0\]

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UnkleRhaukus
  • UnkleRhaukus
\[\frac{\partial M}{\partial y}=\frac {-6}{y^{2}}\qquad\qquad \frac{\partial N}{\partial x}=\frac{2x}{y}-\frac{3y}{x^2}\]\[\qquad\qquad\frac{\partial M}{\partial y}\neq \frac{\partial N}{\partial x}\]
nubeer
  • nubeer
ok..
UnkleRhaukus
  • UnkleRhaukus
\[R=R(x,y)=x^my^n\]
nubeer
  • nubeer
ok this is soemthing new.. is this the general form of the solution?
UnkleRhaukus
  • UnkleRhaukus
im using R for the integrating factor
nubeer
  • nubeer
ok..
UnkleRhaukus
  • UnkleRhaukus
\[\frac{\partial R(x,y)M}{\partial y}\quad= \frac{\partial R(x,y)N}{\partial x}\] using the product rule \[R_y(x,y)M+R(x,y)\frac{\partial M}{\partial y}=R_x(x,y)N+R(x,y)\frac{\partial N}{\partial x}\]
nubeer
  • nubeer
ok i get this much
UnkleRhaukus
  • UnkleRhaukus
\[\small R_y(x,y)\left(3x+\frac 6y\right)+R(x,y)\left(\frac {-6}{y^{2}}\right)=R_x(x,y)\left(\frac {x^2}{y}+\frac{3y}{x}\right)+R(x,y)\left(\frac{2x}{y}-\frac{3y}{x^2}\right)\] \[\small nx^my^{n-1}\left(3x+\frac 6y\right)+x^my^n\left(\frac {-6}{y^{2}}-\frac{2x}{y}+\frac{3y}{x^2}\right)-mx^{m-1}y^n\left(\frac {x^2}{y}+\frac{3y}{x}\right)=0\]
UnkleRhaukus
  • UnkleRhaukus
.... somehow find n and m ,
nubeer
  • nubeer
how? any particular method?
UnkleRhaukus
  • UnkleRhaukus
something to do with the matching indices
nubeer
  • nubeer
hmm still dont get the last part..
UnkleRhaukus
  • UnkleRhaukus
me either
nubeer
  • nubeer
hmm ok its fine but thanks for the help bro.. :) will look on internet
UnkleRhaukus
  • UnkleRhaukus
if you find a really good sight can you tell me please
nubeer
  • nubeer
sure i will let u know..
nubeer
  • nubeer
http://www.cliffsnotes.com/study_guide/Integrating-Factors.topicArticleId-19736,articleId-19711.html @UnkleRhaukus this is a good one but it dont tell for the both x and y .. will post it if i find it

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