Mathematics

The general solution of y" - m2y = 0 is
  • a)
    cj sinh mx + c2 cosh mx
  • b)
    c1 cos mx + c2 sin mx
  • c)
    ccos mx + c2 sinh mx
  • d)
    c1 sin mx + c2 cosh mx
Correct answer is option 'A'. Can you explain this answer?

Ayomide Attah answered  •  4 hours ago
Y''-m^2y=0
r^2-m^2=0 characteristic

r=+-m

y=Ae^mx+Be^-mx
=Ce^mx+De^mx-Ce^-mx+De^-mx(Let A=C+D and B=D-C)
=C(e^mx-e^-mx)+D(e^mx+e^-mx)
=Csinh(mx)+Dcosh(mx)

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