Hey all, i think i'm doing most of this right, but i'm missing a coefficient somewhere when integrating or something...(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Substitute v=y/x into the following differential equation to show that it is homogeneous, and then solve the differential equation.

y'=(3y^2-x^2)/(2xy)

2. Relevant equations

v=y/x

y=xv(x) => y'=v+xv'

v'=dv/dx

3. The attempt at a solution

y'=(3y^2-x^2)/(2xy)

divide top and bottom of right hand side by x^2 to get v's and replace y' by v+xv'

v+xv'=(3v^2-1)/(2v)

subtract v from both sides

xv'=(3v^2-1)/(2v)-v

put the lonely v on a common denominator

xv'=(3v^2-1-2v^2)/(2v)=(v^2-1)/(2v)

separate v's and x's

(2v)dv/(v^2-1)=dx/x

integrate

ln|v^2-1|=ln|x|+c

substitute v=y/x

ln|(y/x)^2-1|=ln|x|+c

simplify

ln|y^2-x^2|=ln|x|+c

the back of the book says the answer is |y^2-x^2|=c|x|^3.

what am i doing wrong? i'm missing a 3 somewhere. i'm kinda rusty with lograthimic algebra, so all help is appreciated. i've gotten a few of these problems wrong by missing a constant or exponent on the right hand of the side of the equation after integrating.

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# Homework Help: V substitution in homogeneous equations (diff eq)

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