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Rudradev Dansena posted an Question
January 18, 2020 • 17:16 pm 15 points
  • IIT JAM
  • Mathematics (MA)

Case ll: When roots of AE are same (repeated) Suppose AE f(m)= 0 has two equal roots (m, = m) m MA m, m, m M In this case the solution will be : If three roots

Case ll: When roots of AE are same (repeated) Suppose AE f(m)= 0 has two equal roots (m, = m) m MA m, m, m M In this case the solution will be : If three roots of AE are equal say m, = m, = m,, then y= (C +C,x)e"* + Ce* +.....+Ce"* Y=(C, +C,X + Cx )ex + C,ema +..... +Cn . is the last statement for 3 roots to be equal is true or there is some misprint in the material?

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  • Priyadarshan Choursiya best-answer

    this is correct. you may here note that here we talk about real roots of m. you can also generalize that result. this result also generalize for complex roots. i.e. if m = a+ib three times and f(m)=0 is 6 degree equation, then y= (e^ax)*[ {c1+c2*x+c3*xx} cos(bx) + {C4+c5*x+c6*xx} sin(bx) ] please see attachment-

    upload_1579338516900.jpg
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