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###### In calculus, one technique used to solve differential equations consists of the separation of variables. For example, consider the equation $x^{2}+3 y \frac{f(y)}{g(x)}=0,$ which is equivalent to $3 y f(y)=-x^{2} g(x) .$ Here each side of the equation contains only one type of variable, either $x$ or $y$ Use the sum and difference identities to separate the variables in each equation. $$\cos (x-y)=0$$

In calculus, one technique used to solve differential equations consists of the separation of variables. For example, consider the equation $x^{2}+3 y \frac{f(y)}{g(x)}=0,$ which is equivalent to $3 y f(y)=-x^{2} g(x) .$ Here each side of the equation contains only one type of variable, either $x$ or $y$ Use the sum and difference identities to separate the variables in each equation. $$\cos (x-y)=0$$

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