Solution to First Order DE Problem - Eliminating Dependent Variable (Solving For y)

 Solve by finding a general solution: 

px ² -  y = 0

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Solve for y:  

y   =  px ²

^{Differentiate:} 

^{dy/dx = y' = p  =}      p ² +  2 px p'   

Rearrange:

2 dp/ (p - 1)   +  dx/x  = 0

è

(p - 1) ²  x  =  c

Eliminating p:

y  -   2  Öyx   +  x  = c

Which is the general solution.