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melmel
 2 years ago
answered question
melmel
 2 years ago
answered question

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

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

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

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

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

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

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

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

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

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

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

UnkleRhaukus
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1http://en.wikipedia.org/wiki/Homogeneous_differential_equation#Homogeneous_functions

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

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

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

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

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

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

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

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

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

UnkleRhaukus
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0always? v=y/x even to other problem?

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

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

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

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