Math for CSTutorial 81 Second Order Differential Equations.

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Presentation transcript:

Math for CSTutorial 81 Second Order Differential Equations

Math for CSTutorial 82 Example 1: Find the general solution of the equation Solution: Since the variable x is missing, set v=y'. The formulas above lead to This a first order separable differential equation. Its resolution givesfirst order separable differential equation Since, we get y' = 0 or

Math for CSTutorial 83 This a first order separable differential equation. Its resolution givesfirst order separable differential equation Since, we get y' = 0 or Since this is a separable first order differential equation, we get, after resolution,separable first order differential equation, where C and are two constants. All the solutions of our initial equation are Note that we should pay special attention to the constant solutions.

Math for CSTutorial 84 Example2 : Find the solution to the IVP Solution: Let us follow the steps: 1 Characteristic equation and its roots Since 4-8 = -4<0, we have complex roots. Therefore, and 2 General solution ;

Math for CSTutorial 85 3 In order to find the particular solution we use the initial conditions to determine and. First, we have. Since, we get From these two equations we get, which implies