11. Find a general solution to the following differential equations.\ a. $4w'' + 3w' - 2w = 0$\ b. $y''' - 2y'' - 12y' + 16y = 0$\ Ans. (a) $w(t) = c_1e^{\frac{1}{8}(-3+\sqrt{41})t} + c_2e^{\frac{1}{8}(-3-\sqrt{41})t}$\ (b) $y(t) = c_1e^{4t} + c_2e^{(-1+\sqrt{5})t} + c_3e^{(-1-\sqrt{5})t}$

Name: 11. Find a general solution to the following differential equations.a. 4w” + 3w' - 2w = 0b. y”' - 2y” - 12y' + 16y = 0Ans. (a) w(t) = c1e^(1)/(8)(-3+√(41))t + c2e^(1)/(8)(-3-√(41))t(b) y(t) = c1e^4t + c2e^(-1+√(5))t + c3e^(-1-√(5))t
Uploaded: 2023-09-21T18:05:46-08:00
Duration: 3 min 2 s
Channel: Adi S
Description: 11. Find a general solution to the following differential equations.a. 4w” + 3w' - 2w = 0b. y”' - 2y” - 12y' + 16y = 0Ans. (a) w(t) = c1e^(1)/(8)(-3+√(41))t + c2e^(1)/(8)(-3-√(41))t(b) y(t) = c1e^4t + c2e^(-1+√(5))t + c3e^(-1-√(5))t

          11. Find a general solution to the following differential equations.\
a. $4w'' + 3w' - 2w = 0$\
b. $y''' - 2y'' - 12y' + 16y = 0$\
Ans. (a) $w(t) = c_1e^{\frac{1}{8}(-3+\sqrt{41})t} + c_2e^{\frac{1}{8}(-3-\sqrt{41})t}$\
(b) $y(t) = c_1e^{4t} + c_2e^{(-1+\sqrt{5})t} + c_3e^{(-1-\sqrt{5})t}$

11. Find a general solution to the following differential equations.a. 4w” + 3w' - 2w = 0b. y”' - 2y” - 12y' + 16y = 0Ans. (a) w(t) = c1e^(1)/(8)(-3+√(41))t + c2e^(1)/(8)(-3-√(41))t(b) y(t) = c1e^4t + c2e^(-1+√(5))t + c3e^(-1-√(5))t

Added by Shane M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/21/2023

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For equation (a): 4r^2 + 3r - 2 = 0 For equation (b): r^3 - 2r^2 - 12r + 16 = 0 Show more…

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Find a general solution to the following differential equations. a. 4w'' + 3w' - 2w = 0 b. y''' - 2y'' - 12y' + 16y = 0 Ans. (a) w(t) = c₁e^((1/8)(-3+√41)t) + c₂e^((1/8)(-3-√41)t) (b) y(t) = c₁e^(4t) + c₂e^((-1+√5)t) + c₃e^((-1-√5)t)