(D2−3D+2)y=e3xAlinearnon−homogeneousODEwithconstantcoefficientshastheformof(anDn+...+a1D+a0)y=g(x)Thegeneralsolutionto(anDn+...+a1D+a0)y=g(x)canbewrittenasy=yh+yphisthesolutiontothehomogeneousODE(anDn+...+a1D+a0)y=0yp,theparticularsolution,isanyfunctionthatsatisfiesthenon−homogeneousequationy=c1e2x+c2exThegeneralsolutiony=yh+ypis:y=c1e2x+c2ex+21e3x
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