y''''+2y'''+6y''+8y'+8y=F(x) why would the solution to the ODE exhibit resonant behaviour when F(x)=cos2x but not when F(x)=sin x?
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The obvious answer- because cos(2x) satisfies the associated homogeneous equation, y''''+ 2y'''+ 6y''+ 8y'+ 8y= 0 and sin(x) does not.
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