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Differential EquationsHardExact Equations & Substitutions

Exact Equations & Substitutions · Hard problem

The equation 2y dx+x dy=02y\,dx+x\,dy=0 has an integrating factor depending on xx alone. Its solution curve through (2,1)(2,1) can be written explicitly as y=f(x)y=f(x) for x>0x>0. Find ∫24f(x) dx\displaystyle\int_2^4 f(x)\,dx.