Slide 1 : Differential Equations. Definition
Slide 2 : ORDER AND DEGREE OF A DIFFERENTIAL EQUATION The order of a differential equation is the order of the highest derivative in the equation. The degree of a differential equation is the highest power to which the derivative of the highest order is raised. Example:
Slide 3 : Solving differential equation The solution or integral of a differential equation is any equation, without derivative or differential, that is defined over an interval and satisfies the differential equation. Example: dy/dx = 5 This differential equation can be satisfied by the equation Y=5x+c. The process of finding y in terms of x is called solving a differential equation.
Slide 4 : Example: Solve the following differential equations. Answer: Y = x 3 + x 2 + c b) Y = x 4 – x -2 +3x +c Note: The above solutions are called general solutions , of the DE’s. If we find the values of c they are called particular solutions .
Slide 5 : Solving differential equation by separating variables The general form
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Slide 7 : Answer:
Slide 8 : S Solve the following Some time it is not possible to separate the variable. Example: Some time it is not possible to separate the variables, as we did In the previous section . We may try to Identify the differential equation as an EXACT equation.
Slide 9 : First order exact differential equations Example:
Slide 10 : First order linear differential equations.
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Slide 12 : Example 1
Slide 13 : Example 2 (Discuss in class).
Slide 14 : TUTORIAL SHEET 1
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Slide 16 : TUTORIAL SHEET 2
Slide 17 :