Question

s Consider the differentiad eqation (a) Find the characteristic equation, determine its roots and their corresponding multiplicities (b) Find a fundamental set of solutions for the differential equation. (c) Find the general solution of the differential equation.
can anyone answer this

Answer 1

yt y'=0 characteristic equation a) is m (m3-1) = n (m-i) (m? 7 m +1)=0 [23-63 = Ca-b) (ahtab +67 m=o (m-1)=0 = m = 1 m +m m= 1&51-4 = -10 312- = + i sz 2 are roots are m=0, 1, -1/2 + 153 6) Fundamental set of solutions - e 12 cos 55 de 2 = & It in 3 x Y = e = 1 YA = ex

c) of m, ma = &#ip, m3, ma then = edx [cicospx + asinpx] + e + cet Mzo na Therefore, the general solution is Xx) = é 12x [cicos se x + C, sin Iz x] + cze & cgex =ce to lose & & Ge 12% in 3 x + (z + C qe 2
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