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Rewrite the differential equation
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$\frac{dy}{dx}=\frac{2x^2+y^2}{3x^2}$
Learn how to solve differential equations problems step by step online. Solve the differential equation 3x^2dy/dx=2x^2+y^2. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{2x^2+y^2}{3x^2} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: y=ux. Expand and simplify.