** Final answer to the problem

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** Step-by-step Solution ** **

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- Exact Differential Equation
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- Integrate by partial fractions
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- FOIL Method
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The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$.

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$\frac{dy}{dx}=y^2-1$

Learn how to solve problems step by step online. Solve the differential equation dy/dx=(y-1)(y+1). The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{y^2-1}dy and replace the result in the differential equation.

** Final answer to the problem ** **

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