Transformation in PDE
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Using the transformation $displaystyle u=frac{w}{y}$ in the PDE: $$xfrac{du}{dx} = u + yfrac{du}{dy}$$ The transformed equation has a solution of the form "$w=?$". What is the method to solve such question? I substituted $displaystyle u=frac{w}{y}$ in the equation and then tried to solve. I got: $$-xfrac{w}{y^2} frac{dy}{dx} = u - frac{w}{y}$$ Is this correct?
pde partial-derivative
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edited Dec 16 '16 at 11:48
Mythomorphic
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asked Dec 16 '16 at 5:41