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## Homework Statement

Use the substitution ##x=X+h## and ##y=Y+k## to transform the equation

##\frac{dy}{dx}=\frac{2x+y-3}{x-2y+1}## to the homogenous equation

##\frac{dY}{dX}=\frac{2X+Y}{X-2Y}##

Find h and k and then solve the given equation

## Homework Equations

## The Attempt at a Solution

If I simply make the substitution into the equation, I get a homogenous equation which I can solve using y=vx substitution. But what I need help understanding is how the ##\frac{dy}{dx}## becomes ##\frac{dY}{dX}## after simply substituting into the LHS?

Is some proof or method of doing this so that I can turn dy/dx into dY/dX and vice versa? The chain rule doesn't help, as I cannot relate X and Y