Transcription of Ch 9 (8 9 09)
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Ch 9 (8 9 09)
Overview(i)An equation involving derivative (derivatives) of the dependent variable withrespect to independent variable (variables) is called a differential equation.(ii)A differential equation involving derivatives of the dependent variable withrespect to only one independent variable is called an ordinary differentialequation and a differential equation involving derivatives with respect to morethan one independent variables is called a partial differential equation.(iii)Order of a differential equation is the order of the highest order derivativeoccurring in the differential equation.(iv)Degree of a differential equation is defined if it is a polynomial equation in itsderivatives.
DIFFERENTIAL EQUATIONS 181 dy dx = 2Ae2x – 2 B.e–2x and 2 2 dy dx = 4Ae2x + 4Be–2x Thus 2 2 dy dx = 4y i.e., 2 dx2 – 4y = 0. Example 2 Find the general solution of the differential equation
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