Seperation of variables - first order PDE

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SUMMARY

The discussion focuses on the method of separation of variables for solving first-order partial differential equations (PDEs). The user initially struggles with the expression X'(x)/X(x) = cx but clarifies that the variables X and x are already separated. The correct approach involves rewriting the left side as (1/X)dX/dx, moving dx to the right side, and integrating to obtain d(X)/X = cxdx.

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[SOLVED] separation of variables - first order PDE

Homework Statement



I have the expression X'(x)/X(x) = cx. How do I separate the variables? It's the fraction on the left side that annoys me.

I know that X'(x) = d(X(x))/dx, but I can't use this here?

EDIT: Sorry for the mis-spelled title. It's "separation".
 
Last edited:
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The variables are X and x and they are basically already separated. The left side is (1/X)dX/dx. Move the dx to right getting d(X)/X=cxdx and integrate.
 
Thanks.
 

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