1. Mathematics for Economics Beatrice Venturi 1 Economics Faculty EXACT: DIFFERENTIAL EQUATIONS Economic Applications LESSON 5 prof. Beatrice Venturi

2. Mathematics for Economics Beatrice Venturi 2 LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS (E.D.O.) Remember that given a function of two variable f(x, y), its totally differential is given by: When the differential is set equal to zero, the resulting equation Is known as an exact differential equation.

3. Mathematics for Economics Beatrice Venturi 3 EXACT DIFFERENTIAL EQUATIONS. For instance given: The total differential is is exact. Thus the differential equations

4. Mathematics for Economics Beatrice Venturi 4 EXACT DIFFERENTIAL EQUATIONS. In general a differential equation : The test of exactness or is exact if and only if exist a function f(y,t) such that:

5. Mathematics for Economics Beatrice Venturi 5 EXACT DIFFERENTIAL EQUATIONS Method of solution. It follows from: That: Example:

6. Mathematics for Economics Beatrice Venturi 6 EXACT DIFFERENTIAL EQUATIONS Method of solution. It follows from: That: Example:

7. EXACT DIFFERENTIAL EQUATIONS Mathematics for Economics Beatrice Venturi 7 but then