I solve differential equations but don't understand why am I solving this. I mean, what is the relation? If I solve for y^2=4ax, and I get 2xy'-y=0 as the DE, then what does it imply? What does it actually mean? How can I use this differential equation practically, or by any means?
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what does the differential equation of y^2=4ax mean?
2y dy/dx = 4a
dy/dx = 2a / y = 2a / [4ax]^(1/2)
dy/dx = a^(1/2) / x^(1/2)