Ordinary Differential Equation

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Presentation transcript:

Ordinary Differential Equation

Definition of Deferential Equation A equation is called deferential equation if it contains a dependent variable, independent variable and derivative of dependent variable. Ex:-

Order of Differential Equation:- The order of differential equation is the highest order derivative in the differential equation is called order of differential equation. Ex. As in the above given equation the highest order derivative is of second order so the order of differential equation is 2.

Degree of differential equation A degree of differential equation is the quotient(power) of highest order derivative is called degree of differential equation. Ex. As in the above given equation the quotient of highest order derivative is 4 so the degree of differential equation is 4.

Linear and nonlinear differential equation A differential Equation is called linear if degree of each derivative is one and degree of dependent variable is one also there is not the product of dependent variable and its derivative is called linear differential equation otherwise it is called nonlinear differential equation. Ex.

As the degree of each derivative is one and there is no product of dependent variable and derivative of dependent variable so the differential equation is linear. Ex. Here the degree of derivative is 4 so it is not a linear differential equation.

Formation of differential equation For the formation of differential equation form a given equation of curve differentiate the curve as many time as the number of arbitrary constant in the curve equation and remove the arbitrary constant. Ex. Differentiate the above given curve once .

It is the required differential equation.

To form equation of curve from a differential equation By using separation of variable method In this method firstly separate the variable then integrate on both side. Ex:- Which is the required equation of curve.