?The equation \(y^{\prime \prime}+y^{\prime}-2 y=x^2\) is called a differential equation

Chapter 2, Problem 72

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The equation \(y^{\prime \prime}+y^{\prime}-2 y=x^2\) is called a differential equation because it involves an unknown function y and its derivatives \(y^{\prime}\) and \(y^{\prime \prime}\). Find constants A, B, and C such that the function \(y=A x^2+B x+C\) satisfies this equation. (Differential equations will be studied in detail in Chapter 9.)

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