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Differential EquationsChallengeExact Equations & Substitutions

Exact Equations & Substitutions · Challenge problem

The equation (x+3y) dx+(3x+y) dy=0(x + 3y)\,dx + (3x + y)\,dy = 0 is exact. Let y(x)y(x) be its solution with y(1)=0y(1) = 0. Find lim⁡x→∞y(x)x\displaystyle\lim_{x \to \infty} \dfrac{y(x)}{x}.