5014 - Differential Equations BC CALCULUS. Differential Equations Defn: An equation that contains a derivative ( or a function and a derivative ) is called.

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Differential Equations BC CALCULUS

Differential Equations Defn: An equation that contains a derivative ( or a function and a derivative ) is called a Differential Equation. EX: or The most famous might be: AP requires only Separable Diff Eq’s.

Type A: Explicit We did these last semester as Initial Value Problems with Anti- derivatives. Illustration: “Separate the variables” or Write in Differential form. Integrate both sides. Add the +c’s and put on the dominant side.

Type B: Implicit AP requires only “separable.” Illustration:

Example: Find the GENERAL and PARTICULAR Solutions.

Example 2: 1973 AB Exam. If and y = 4 when x = 0, then y =

Example: AP Type Find the GENERAL and PARTICULAR Solutions. BREAK HERE IN CASE OF EMERGENCY ! REM: the Diff.Eq. must be a product !

Example 2: AP Type Find the GENERAL Solution.

Example 3: AP Type Find the PARTICULAR Solution.

VERIFY Objective: To show (verify) a given function is a solution to a Differential Equation. Rem: ALGEBRA I To show a point is a solution to a system of equations, plug in the point and check if the equations are true or false. Is ( 2, -3 ) a solution to

Illustration: Objective: To show (verify) a given function is a solution to a Differential Equation. Illustration: Show is a solution to. Find and substitute both y and into the equation.

Example: Verify that is a solution to

DAY ONE: TEXT6.1 p odd 6.4 p odd