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Problem 68 Hard Difficulty

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


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Hey, it's clear something. You re here. And so we have our first derivative, which is to a x plus be And we have our second derivative, which is equal to to a We're gonna plug this into our equation when we get to a plus to a X plus being lying us too Times a x square plus d x plus c. Then we're gonna rearrange the terms. On the right side, we get negative to a X square plus two a minus to be thanks close to a plus B minus. To see the coefficient of X square has to be equal on both sides. So we get a is equal to negative 1/2 and V is equal to negative 1/2 as well. Then we have zero is equal to to a plus being Linus to see you got to see a sequel to Negative three house After we plug in values for and be so we get wise equal to negative 1/2 X square, minus 1/2 Thanks minus 3/4. Since when we simple finest become C is equal to negative three forts Oh,