Given the coupled system x\' + y = 3, y\' - 6x = 4, a corresponding second order

Question

Given the coupled system

x' + y = 3,

y' - 6x = 4,

a corresponding second order ODE in y alone would be Question 6 options: A) y'' + 6y = -18 B) y'' + 6y = -9 C) y'' + 6y = -6 D) y'' + 6y = -3 E) y'' + 6y = 3 F) y'' + 6y = 6 G) y'' + 6y = 9 H) y'' + 6y = 18 I) none of these
Please show work!! Given the coupled system

x' + y = 3,

y' - 6x = 4,

a corresponding second order ODE in y alone would be Given the coupled system

x' + y = 3,

y' - 6x = 4,

a corresponding second order ODE in y alone would be A) y'' + 6y = -18 B) y'' + 6y = -9 C) y'' + 6y = -6 D) y'' + 6y = -3 E) y'' + 6y = 3 F) y'' + 6y = 6 G) y'' + 6y = 9 H) y'' + 6y = 18 I) none of these
A) y'' + 6y = -18 B) y'' + 6y = -9 C) y'' + 6y = -6 D) y'' + 6y = -3 E) y'' + 6y = 3 F) y'' + 6y = 6 G) y'' + 6y = 9 H) y'' + 6y = 18 I) none of these Please show work!! A) y'' + 6y = -18 B) y'' + 6y = -9 C) y'' + 6y = -6 D) y'' + 6y = -3 E) y'' + 6y = 3 F) y'' + 6y = 6 G) y'' + 6y = 9 H) y'' + 6y = 18 I) none of these

Explanation / Answer

y' - 6x = 4

differentiate

y'' - 6x' = 0

put x' + y = 3 ==> x' = 3 - y

y'' - 6*(3- y) = 0

=>

y'' + 6y = 18

H) y'' + 6y = 18

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