Differential Equations MATH 225
Colorado School of Mines
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Date Created: 10/05/15
18 Linearity Principles Linearity Principle If yht is a solution of the homogeneous linear equation dy may or i g my 0 then kyht is a solution for any constant k Extended Linearity Principle Consider the nonhomogeneous equation d d z aty bt and its associated homogeneous equation d y aty O 1 If yht is any solution to the homogeneous equation and ypt is any solution to the nonhomogeneous equation then yht ypt is also a solution of the nonhomogeneous equation 2 Suppose ypt and yqt are two solutions of the nonhomogeneous equation then ypt yqt is a solution of the homogenous equation Therefore if yht is nonzero kyht ypt is the general solution of the nonhomogeneous equation