Differential equation dx/x(z-2y^2) = dy/y(z-y^2-2x^3) = dz/z(z-y^2-2x^3)

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SUMMARY

The discussion focuses on solving the differential equation represented as dx/x(z-2y²) = dy/y(z-y²-2x³) = dz/z(z-y²-2x³). The user successfully derived one solution, y = cz, by integrating the equation dy/y(z-y²-2x³) = dz/z(z-y²-2x³). They are now seeking further assistance to find additional solutions by substituting y with cz in the equation dx/x(z-2y²) = dz/z(z-y²-2x³).

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Homework Statement



Solve
dx/x(z-2y^2) = dy/y(z-y^2-2x^3) = dz/z(z-y^2-2x^3)



Homework Equations





The Attempt at a Solution


i got one solution by taking

dy/y(z-y^2-2x^3) = dz/z(z-y^2-2x^3)

dy/y= dz/z
integ: to bothsides

ln y = ln z + ln c
ln y = ln (zc)
y=zc

y/z= c

now i am looking for next solution kindly help.
 
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Now, you can replace y by cz in
[tex]\frac{dx}{x(z-2y^2)}= \frac{dz}{z(z- y^2- 2x^3)}[/tex]
 

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