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Differential Equations
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OpenStudy (anonymous):
What is the general solution to y''''+y=0? I get to the characteristic equation (r^2+i)(r^2-i)=0. Using the Wolframalpha website to find the roots I get r1 = +(-1)^1/4, r2 = -(-1)^1/4, r3 = +(-1)^3/4 and r4 = -(-1)^3/4. I have a feeling its going to be in some form of sine & cosine (have done 2nd order ODE's) but am at a loss to get to the exact solution for this 4th order ODE. I would appreciate any guidance!
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