Question

YOU MUST SHOW SUPPORTING WORK TO RECEIVE CREDIT Solve the following: 1) $y'' + 4y' + 4y = 6sin(3x)$ 2) $y'' + 3y' + 2y = 4e^{-2x}$ 3) $y'' - 2y' + y = xe^x$ 4) $y'' - 2y' + y = x^5$ 5) $y'' - 2y' + y = e^x/x^5$

          YOU MUST SHOW SUPPORTING WORK TO RECEIVE CREDIT
Solve the following:
1) $y'' + 4y' + 4y = 6sin(3x)$
2) $y'' + 3y' + 2y = 4e^{-2x}$
3) $y'' - 2y' + y = xe^x$
4) $y'' - 2y' + y = x^5$
5) $y'' - 2y' + y = e^x/x^5$

Added by Stephen L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Lauren Shelton

12/20/2021

Step 1

1) Characteristic equation: r^2 + 4r + 4 = 0 This equation has a repeated root at r = -2. Therefore, the complementary solution is y_c = c1e^(-2x) + c2xe^(-2x) 2) Characteristic equation: r^2 + 3r + 2 = 0 This equation has roots at r = -1 and r = -2. Show more…

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Solve the following: 1) y'' + 4y' + 4y = 6sin(3x) 2) y'' + 3y' + 2y = 4e^(-2x) 3) y'' - 2y' + y = xe^(x) 4) y'' - 2y' + y = x^(-5) 5) y'' - 2y' + y = (e^(x))/(x^(5)) GWORK TO RECEIVE CREDIT