Determine whether the given differential equation is homogeneous, and if so find the general solution. (If the equation is not homogeneous, enter NOT HOMOGENEOUS.) x(x + y)y' = y(x - y)
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Step 1: Rewrite the given differential equation as \(x(x + y)y' = y(x - y)\). Show more…
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Solve the homogeneous differential equation in terms of $x$ and $y .$ A homogeneous differential equation is an equation of the form $M(x, y) d x+N(x, y) d y=0,$ where $M$ and $N$ are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions $y=v x$ and $d y=x d v+v d x$ $$(x-y) d x-(x+y) d y=0$$
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