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The equation2x^2 3y^2 = xycan be written in the form y = f(ylx), i.e., it is homogeneous, so we can use the substitution u = ylx to obtain a separable equation with dependent variable u = u(x):Introducing this substitution and using the fact that y = xu u, we can write (*) asy = xu' u = f(u) where f(u)Separating variables, we can write the equation in the formdx/g(u) = duwhere g(u)An implicit general solution with dependent variable u can be written in the formTransforming y = ylx back int
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