What is the integral of dydx=y^2/x^2

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The integral of the differential equation dy/dx = y^2/x^2 can be solved using the method of separation of variables. By rewriting the equation as y'/y^2 = 1/x^2, and applying the chain rule, the solution is derived as y = 1/[(1/x) + C], where C is a constant. This method is fundamental in solving first-order differential equations and is discussed in detail in differential equations textbooks.

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im having problem integrating the equation

dydx=y^2/x^2

and also

dydx=3*y^2/x
 
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I'm assuming they should be dy/dx=y^2/x^2
and dy/dx=3*y^2/x .

Your differential equations textbook should discuss "separation of variables" near the very beginning.
 
This can be rewritten in this way:
y'=y^2/x^2 with x different from zero.
y'/y^2=1/x^2
using chain rule:
d/dx[-1/y]=d/dx[-(1/x)+C]
consequentely:
1/y=(1/x)-C
y=1/[(1/x)+C]
 

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