Question

What is the value of b for the equation d²-4=0​

Answer 1

Answer:

It is a homogeneous linear differential equation of IV order with constant coefficients and so is easy to solve. The corresponding auxiliary equation is m^4 + 1 = 0, whose roots are the four complex 4th roots of (-1) = cos(pi) + i sin(pi). These are

cos(pi/4) (+/-) i sin (pi/4) = (1/sqrt 2) +/- i/sqrt 2 and

cos (3.pi/4) (+/-) i sin(3.pi/4) = (-1/sqrt 2) +/- i/sqrt 2. .

Accordingly a general solution (i.e. Complementary Function) is

y = e^(x/sqrt 2)[A cos (x/sqrt 2) + B sin (x/sqrt 2)] +

e^(-x/sqrt/2)[C cos(x/sqrt 2) + D sin(x/sqrt 2)].

Step-by-step explanation:

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