this is the given equation(adsbygoogle = window.adsbygoogle || []).push({});

y'=(4y-3x)/(2x-y)

and here is all the work i've done so far:

(4v-3)/(2-v)=v+x*dv/dx

i moved v over and came up with this

(-3+2v+v^2)/(2-v)=x*dv/dx

did a flip

(2-v)/(-3+2v+v^2)dv=dx/x

by partial fractions I got a=-3/2 and b=1/2

so -3/2*ln|v-1|+1/2*ln|v+3|+c=ln|x|

after making the -3/2 and 1/2 powers to ln and throwing e in

(v-1)^(-3/2)+(v+3)^(1/2)+c=x

or

((y+x)/x)^(-3/2)+((y+3x)/x)^(1/2)+c=x

that's the part I'm stuck at.

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# Homogeneous equation, problem with algebra

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