Mr. Integral
Math notes/Differential Equations/Second-Order Linear Equations

Superposition and Fundamental Solutions — Cheat sheet

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Core rule

y=yh+yp,y=y_h+y_p, yh=c1y1+c2y2.y_h=c_1y_1+c_2y_2.

Watch for

Superposition applies to homogeneous linear equations. Adding two solutions with the same nonzero forcing doubles that forcing. Nonlinear equations generally do not allow superposition at all.