💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

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.)

Answer

More Answers

Discussion

You must be signed in to discuss.

Video Transcript

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,