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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)
 one year ago
 one year ago
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)
 one year ago
 one year ago

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UnkleRhaukusBest ResponseYou've already chosen the best response.1
do you have an example we can work through /
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
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.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\left(3x+\frac 6y\right)\text dx+\left(\frac {x^2}{y}+\frac{3y}{x}\right)\text dy =0\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\frac{\partial M}{\partial y}=\frac {6}{y^{2}}\qquad\qquad \frac{\partial N}{\partial x}=\frac{2x}{y}\frac{3y}{x^2}\]\[\qquad\qquad\frac{\partial M}{\partial y}\neq \frac{\partial N}{\partial x}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[R=R(x,y)=x^my^n\]
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
ok this is soemthing new.. is this the general form of the solution?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
im using R for the integrating factor
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\frac{\partial R(x,y)M}{\partial y}\quad= \frac{\partial R(x,y)N}{\partial x}\] using the product rule \[R_y(x,y)M+R(x,y)\frac{\partial M}{\partial y}=R_x(x,y)N+R(x,y)\frac{\partial N}{\partial x}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\small R_y(x,y)\left(3x+\frac 6y\right)+R(x,y)\left(\frac {6}{y^{2}}\right)=R_x(x,y)\left(\frac {x^2}{y}+\frac{3y}{x}\right)+R(x,y)\left(\frac{2x}{y}\frac{3y}{x^2}\right)\] \[\small nx^my^{n1}\left(3x+\frac 6y\right)+x^my^n\left(\frac {6}{y^{2}}\frac{2x}{y}+\frac{3y}{x^2}\right)mx^{m1}y^n\left(\frac {x^2}{y}+\frac{3y}{x}\right)=0\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
.... somehow find n and m ,
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
how? any particular method?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
something to do with the matching indices
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
hmm still dont get the last part..
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
hmm ok its fine but thanks for the help bro.. :) will look on internet
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
if you find a really good sight can you tell me please
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
sure i will let u know..
 one year ago

nubeerBest ResponseYou've already chosen the best response.0
http://www.cliffsnotes.com/study_guide/IntegratingFactors.topicArticleId19736,articleId19711.html @UnkleRhaukus this is a good one but it dont tell for the both x and y .. will post it if i find it
 one year ago
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