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• 00:34, 18 May 2024 Rice talk contribs created page Superposition principle (Created page with "Category:Differential Equations The '''superposition principle''' is actually a broad category of principles that widely apply to homogeneous linear stuff. I'll discuss this in the context of differential equations. Consider a linear operator on functions, L <math> L[y]=y''+py'+qy </math> It can be (pretty easily) proven that <math> L[y_1+y_2]=L[y_1]+L[y_2] </math> and <math> L[cy]=cL[y] </math> Then, given two homogeneous solutions <math> L[y_1]=L[y_2]=...")