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nTH oRDER Linear equation
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Determine if linear or non-linear, homogeneous or nonhomogeneous, with constant or variable coefficients.
If the root λ is repeated k time, the solution corresponding to this is
xλ1kk21 e)xc...xcc(y
If the pair of roots λ1,2 = a ± bi is a complex, conjugate pair, the solution corresponding to this is
)bxsincbxcosc(ey 21ax
General Solution of the Homogeneous, Linear ODE with Constant Coefficients
The general solution of the homogeneous linear ODE with constant coefficients is the linear combination of the above solutions.