For extra points to be added to your final exani score (even if it goes above 10

Question

For extra points to be added to your final exani score (even if it goes above 100) have some fun and learn more about variation of parameters for higher order ordinary differential equations. Extend the formulas we figured out in class for variation of parameters. That is, we already know that if y1 and y2 are linearly independent solutions to the differential equation y' + p(t)/ + q(t)y = 0 then we can find a particular solution. w, (t)y¡ (t) + u2 (t)y2 (t) to y" + p(t)y' + q(t)y = g(t) by using the formulas where For 2 points. find the correct formulas to find a particular solution to the differential equation y" + p(t) ym + q(t)y' + r(t)y = g(t) assuming we already have linearly independent solutions y1, y2, and y3 to the associated homogeneous equation. Show your work. For an additional 1 point make the formulas as nice as possible. ("Nice" means you must use Cramer's rule and write them using various Wronskians.)

Explanation / Answer

answer to question 1

refer these pics:

"https://drive.google.com/file/d/0B2N5Vr-uYjprLVo1aTM5cFBwV0k/edit?usp=sharing"

"https://drive.google.com/file/d/0B2N5Vr-uYjprYllMYlVnVi1qdjQ/edit?usp=sharing"

"https://drive.google.com/file/d/0B2N5Vr-uYjpraGM2Z0oxREFTa3M/edit?usp=sharing"

"https://drive.google.com/file/d/0B2N5Vr-uYjprWDJxeFR1SE1tcE0/edit?usp=sharing"

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