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Second Order Differential Equation Non Homogeneous

Class Notes 5: Second Order Differential Equation Non Homogeneous 82A Engineering Mathematics Second Order Linear Differential equations Homogeneous & Non Homogenous v p, q, g are given, continuous functions on the open interval I )(0)()(tgytqytpyHomogeneousNon-homogeneo us Solution:where yc(x): solution of the Homogeneous Equation (complementary solution)yp(x): anysolution of the non- Homogeneous Equation (particular solution) sHomogeneoushomogeneou-Non , 0 , )()()(xgyxqyxpy)()(xyxyypc Second Order Linear Differential equations Homogeneous & Non Homogenous Structure of the General Solution 00)0()0( ytyyty Order Linear Differential equations Non Homogenous )()()(tftqytpy 00)0()0( ytyyty ( ) If Y1and Y2are solutions of the nonhomogeneous Equation Then Y1 -Y2is a solution of the Homogeneous Equation If, in addition, {y1, y2} forms a fundamental solution set of the Homogeneous Equation , then there exist constants c1and c2 such that)()()()(221121tyctyctYtY )()()(tgytqytpy 0)()( ytqytpyTheorem ( )

equations for which we can easily write down the correct form of the particular solution Y(t) in advanced for which the Nonhomogenous term is restricted to •Polynomic •Exponential •Trigonematirc (sin / cos ) Second Order Linear Non Homogenous Differential Equations – Method of Undermined Coefficients –Block Diagram

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