Question

the c.f for (D^2+1)y=0
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Answer 1

Answer:

Your equation is

x4+x2+1=0

Let y=x2, then we have that:

y2+y+1=0

And the solution is y=−12±3√2i, or in exponential form: y1=e23iπ and y2=e−23iπ. And from x2=y, we get that x12=exp(23iπ+2niπ2) and x34=exp(−23iπ+2niπ2) for n=0 and n=1. So the roots are:

x1=exp(13iπ)

x2=exp(43iπ)

x3=exp(−13iπ)=exp(53iπ)

x4=exp(23iπ)