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Chapter 5 – Simplifying Formulas and Solving Equations
Chapter 5 – Simplifying Formulas and Solving Equations

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... Therefore, the general solution to the homogeneous equation is c1 e−x + c2 e−2x . To guess a solution to the non-homogeneous equation, we try y = Ax2 + Bx + C. Calculating the derivatives, we have y 0 = 2Ax + B y 00 = 2A Plugging these values into the non-homogeneous equation gives us y 00 + 3y 0 + ...
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History of algebra

As a branch of mathematics, algebra emerged at the end of 16th century in Europe, with the work of François Viète. Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.This article describes the history of the theory of equations, called here ""algebra"", from the origins to the emergence of algebra as a separate area of mathematics.
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