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melmel
 one year ago
answered question
melmel
 one year ago
answered question

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UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2what do you get if you re arrange to dy/dx=

melmel
 one year ago
Best ResponseYou've already chosen the best response.0sorry but i dont know .................it equal to 1 dont know if I am correct >.<

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2after your get the left hand side to be dy/dx sub v=y/x

melmel
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ xdy }{ yxdx }=1\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah, now move the other terms to the other side

melmel
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ dx }= \frac{ yx }{ x }\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2\[(yx)/x = y/x  x/x\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2x/x simplifies to ...

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

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2use the product rule to find y'

melmel
 one year ago
Best ResponseYou've already chosen the best response.0\[y'=v(1) x\frac{dv }{ dx }\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2should be plus not minus

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

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2which is now variables separable

melmel
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dv }{ dx }= \frac{ v ^{2} v}{ x }\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2um you should have taken away the v from both sides, before dividing by x

oldrin.bataku
 one year ago
Best 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. \(dy=\left(x\dfrac{dv}{dx}+v\right)\,dx\):$$(xvx)dx+x(x\,dv+v\,dx)=0\\(xvx)\,dx+x^2dv+vx\,dx=0\\x\,dx+x^2\,dv=0\\x^2\,dv=x\,dx\\dv=\frac1x\,dx\\v=\log x+C\\y/x=\log x+C\\y=x\log x+Cx$$

oldrin.bataku
 one year ago
Best ResponseYou've already chosen the best response.1http://en.wikipedia.org/wiki/Homogeneous_differential_equation#Homogeneous_functions

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

melmel
 one year ago
Best ResponseYou've already chosen the best response.0then identify if its exact DE or not

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

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2What is the second thing? where does the dx go?

melmel
 one year ago
Best ResponseYou've already chosen the best response.0v= lnx +c is that right?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yes, now remember v=y/x

melmel
 one year ago
Best ResponseYou've already chosen the best response.0then sub v= y/x to v =ln x +c

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2thats better \(\checkmark\)

melmel
 one year ago
Best ResponseYou've already chosen the best response.0tnx i other one here tech me ?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2is there an equals sign somewhere?

melmel
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ dx }=\frac{ x }{ y }\]

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

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

melmel
 one year ago
Best ResponseYou've already chosen the best response.0always? v=y/x even to other problem?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2When 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

melmel
 one year ago
Best ResponseYou've already chosen the best response.0can you gve to me the final answer here this will serve as my basis

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2sometimes a 'homogenous equations" means something else

melmel
 one year ago
Best ResponseYou've already chosen the best response.0you gve a sense to me :)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2i haven't worked out the final answer yet

melmel
 one year ago
Best ResponseYou've already chosen the best response.0by the way thank you :))) tnz alot
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