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- Equazione differenziale esatta
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Rewrite the differential equation using Leibniz notation
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$x^2\frac{dy}{dx}=4x^2+7xy+2y^2$
Learn how to solve problems step by step online. x^2y^'=4x^2+7xy2y^2. Rewrite the differential equation using Leibniz notation. Apply the formula: a\frac{dy}{dx}=c\to \frac{dy}{dx}=\frac{c}{a}, where a=x^2 and c=4x^2+7xy+2y^2. We can identify that the differential equation \frac{dy}{dx}=\frac{4x^2+7xy+2y^2}{x^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.
