Given the ODE (yx+y^2)dx - x^2dy=0 Write the equation in the form y\' = f(x/y)=_

Question

Given the ODE (yx+y^2)dx - x^2dy=0 Write the equation in the form y' = f(x/y)=__________________ . Next use the substitution u=(y/x) to write the equation as an ODE with independent variable x and dependent variable u , i.e., in the form u' = (f(u)-u)/x Notice that this equation is separable. If we separate the variables we obtain two separate integrals ( Do not add an arbitrary constant as we already put one there.) ): and Converting back to the original variables x and y leads to an implicit general solution which can be written as ln(x) + ______ = C

Explanation / Answer

(yx+y^2)dx - x^2dy = 0

y' = (yx+y^2)/x^2

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