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![[Post New]](/templates/default/images/icon_minipost_new.gif) 16 Mar 2008 20:25:20 IST
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(1+xy)ydx+(1-xy)xdy=0
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16 Mar 2008 20:35:58 IST
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The exp. is
=>ydx+xdy+xy2dx-x2ydy=0.
=>d(xy)+xy(ydx-xdy)=0
=>d(xy)+x/y*d(x/y)=0..
Integrating both sides,
=>xy+(x2/2y2)+c=0
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MaNuTd RoXxXx..MaNuTd 2 WiN PrEmIeR LeAgUe ThIs SeAsOn ToO AlOnG WiTh ChAmPiOnS LeAgUe.....HaiL RoNaLdO ...HaiL LaMpArD... |
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16 Mar 2008 20:39:42 IST
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I DID NOT UNDERSTAND WAT U HAVE DONE MAKE IT MORE CLEAR PLS!!
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16 Mar 2008 20:40:31 IST
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which step??
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16 Mar 2008 20:44:26 IST
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SECOND STEP.. WHICH FORM S IT DY/DX OR DX/DY
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16 Mar 2008 20:46:30 IST
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Hi Vinod
Ans is wrong
It is -1/xy=log(y/x)+C
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16 Mar 2008 20:47:54 IST
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CAN YOU DO THE WHOLE THING PL.S PLS
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16 Mar 2008 20:48:08 IST
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Here is d method
ydx+xdy+xy(ydx-xdy)=0
write it as
d(xy)/xy=xdy-ydx
d(xy)/(xy)^2=d(log(y/x)
nudge if not clear
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16 Mar 2008 20:49:45 IST
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d(xy) is same as xdy + ydx...
the term xy(ydx-xdy) cannot be written in a form as above..so,multiply and divide by y2,u get (x/y)*(ydx-xdy)/y2...
now (ydx-xdy)/y2 is d(x/y)...
so the exp. has now become (x/y)*d(x/y)...
this is same as tdt,where t is x/y...
so integral is t2/2...
so the answer is
xy+(x2/2y2)+c=0
Do you have anymore doubts??
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16 Mar 2008 20:59:09 IST
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WHAT S D(X/Y)
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16 Mar 2008 21:00:19 IST
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![[tex] \\ \mbox{given question can be rewritten as } \\ (ydx+xdy) = xy(xdy-ydx) \\ \mbox{now} \\ xdy+ydx = d(xy) \\ \mbox{bring the xy down and multiply and divide by another xy on both sides} \\ \mbox{now the question looks like} \\ \frac{1} {(xy)^2} \*d(xy) = \frac{(xdy-ydx)} {xy} \\ \mbox{LHS put } \ xy=t \ \mbox{and integrate and RHS is nothing but} \ d(\log(\frac{y}{x})) \\ \mbox{so integrating both sides we get} \\ \frac{-1}{xy} = \log(\frac{y}{x}) + c](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/5/3/8/53845e7d69ba46a156e99d18eb7fccd77d336cca.gif)
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16 Mar 2008 21:09:05 IST
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even my method looks correct..den why diff. answers???
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16 Mar 2008 21:42:39 IST
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the term xy(ydx-xdy) cannot be written in a form as above..so,multiply and divide by y2,u get (x/y)*(ydx-xdy)/y2...
Here lies ur mistake Lampard
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