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Week_04_4.2,4.3

# Week_04_4.2,4.3 - MATH2860U Chapter 4 cont 1 HIGHER-ORDER...

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MATH2860U: Chapter 4 cont… 1 HIGHER-ORDER DIFFERENTIAL EQUATIONS cont… Reduction of Order (Section 4.2 of Zill and Cullen, pg. 130) Recall: We’ve just spent time studying solutions to linear 2 nd order differential equations, and found that their solution could be expressed as 2 2 1 1 y c y c y where 1 y and 2 y are linearly independent solutions. Let’s explore this by considering a simple example: Suppose that we know that x e x y 3 1 ) ( is a solution to 0 9 6 y y y …what is a 2 nd linearly independent solution? This technique used in the above example is known as the method of reduction of order.

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MATH2860U: Chapter 4 cont… 2 Question: What did we just do, and why did it work? Question: Will we have to go through this lengthy process each time? Theorem: For a 2 nd order differential equation in standard form 0 ) ( ) ( y x Q y x P y , if one solution ) ( 1 x y is known, then reduction of order
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Week_04_4.2,4.3 - MATH2860U Chapter 4 cont 1 HIGHER-ORDER...

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