Question

please solve problem (B)

Every student has to submit the answers by Thursday 04 April 2019. stion L: Let y be a ftunction of s. Find a generalsolution to he iven diffentiad quatio da

Answer 1

B). Given differential equation is

"B). Given differential equation is y^4 - 12 y""' + 27 y"" + 40 y' = 0 Auxiliary equation is m^4 - 12 m^3 + 27 m^2 + 40 m = 0 m(m^3 - 12 m^2 + 27 m + 40) = 0 m = 0, m^3 - 12 m^2 + 27 m + 40 if m^3 - 12 m^2 + 27 m + 40 = 0 m^2 (m - 1) - 13 m (m + 1) + 40 (m + 1) = 0 (m + 1) (m^2 - 13 m + 40) = 0 (m + 1) (m - 8) (m - 5) = 0 m = -1, 8, 5 Hence, general solution is y(x) = A e degree + B e^- x + C e^5x + D e^8x y(x) = A + B e^- x + C e^5x + D e^8x "

Auxiliary equation is

$m^4-12m^3+27m^2+40m=0$

$m(m^3-12m^2+27m+40)=0$

If

$m^3-12m^2+27m+40=0$

$m=-1,8,5$

Hence, general solution is

$y(x)=Ae^0+Be^{-x}+Ce^{5x}+De^{8x}$

$y(x)=A+Be^{-x}+Ce^{5x}+De^{8x}$