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.(v)Degree (when defined) of a differential equation is the highest power (positiveinteger only) of the highest order derivative in it.(vi)A relation between involved variables, which satisfy the given differentialequation is called its solution. The solution which contains as many arbitraryconstants as the order of the differential equation is called the general solutionand the solution free from arbitrary constants is called particular solution.

182 MATHEMATICS y.x = xx dx2, i.e. yx = 4 4 x +c Hence y = 3 4 xc x +. Example 5 Find the differential equation of the family of lines through the origin. Solution Let y = mx be the family of lines through origin. Therefore, dy dx = m Eliminating m, we get y = dy dx. x or x dy dx – y = 0. Example 6 Find the differential equation of all non-horizontal …

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