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UnkleRhaukusBest ResponseYou've already chosen the best response.2
what do you get if you re arrange to dy/dx=
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
sorry but i dont know .................it equal to 1 dont know if I am correct >.<
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
after your get the left hand side to be dy/dx sub v=y/x
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
\[\frac{ xdy }{ yxdx }=1\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
yeah, now move the other terms to the other side
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
\[\frac{ dy }{ dx }= \frac{ yx }{ x }\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
\[(yx)/x = y/x  x/x\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
x/x simplifies to ...
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
good so you have \[\frac{dy}{dx}=\frac yx1\] now let \(y/x=v\) \(y=vx\) \(y'=?\)
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
use the product rule to find y'
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
\[y'=v(1) x\frac{dv }{ dx }\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
should be plus not minus
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
now sub this in \[\frac{dy}{dx}=y/x1\] becomes \[v+x\frac{dv}{dx}=v1\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
which is now variables separable
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
\[\frac{ dv }{ dx }= \frac{ v ^{2} v}{ x }\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
um you should have taken away the v from both sides, before dividing by x
 8 months ago

oldrin.batakuBest ResponseYou've already chosen the best response.1
$$(xy)\,dx+x\,dy=0$$note this is homogeneous; both our functions \(xy,x\) are homogeneous. as @UnkleRhaukus stated, use a substitution \(y=vx\) i.e. \(dy=\left(x\dfrac{dv}{dx}+v\right)\,dx\):$$(xvx)dx+x(x\,dv+v\,dx)=0\\(xvx)\,dx+x^2dv+vx\,dx=0\\x\,dx+x^2\,dv=0\\x^2\,dv=x\,dx\\dv=\frac1x\,dx\\v=\log x+C\\y/x=\log x+C\\y=x\log x+Cx$$
 8 months ago

oldrin.batakuBest ResponseYou've already chosen the best response.1
http://en.wikipedia.org/wiki/Homogeneous_differential_equation#Homogeneous_functions
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
guys can be this one \[xdv=(v ^{2}v) dx .....then....... (v ^{2}v)xdv=0\]
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
then identify if its exact DE or not
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
\[v+x\frac{dv}{dx}=v1\\ x\frac{dv}{dx}=1\\dv=xdx\\ \\∫dv=∫dx/x\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
What is the second thing? where does the dx go?
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
v= lnx +c is that right?
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
yes, now remember v=y/x
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
then sub v= y/x to v =ln x +c
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
thats better \(\checkmark\)
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
tnx i other one here tech me ?
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
is there an equals sign somewhere?
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
\[\frac{ dy }{ dx }=\frac{ x }{ y }\]
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
ok this one is the same technique, rearrange to dy/dx= and substitute v=y/x
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
divide both sides of the fraction by x, to get it in the right form \[\frac{x}{y2x}=\frac{x/x}{y/x2x/x }\]
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
always? v=y/x even to other problem?
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
When we can express the DE as y'(x) = f (y/x) we can call this a homogenous equation and v = y/x substitution will work if we can't get this form y'(x) = f (y/x) this technique wont work
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
can you gve to me the final answer here this will serve as my basis
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
sometimes a 'homogenous equations" means something else
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
you gve a sense to me :)
 8 months ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
i haven't worked out the final answer yet
 8 months ago

melmelBest ResponseYou've already chosen the best response.0
by the way thank you :))) tnz alot
 8 months ago
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