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IB DP Maths: AI HL復習筆記5.7.2 Second Order Differential Equations

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月22日 下午3:36

Euler's Method: Second Order

How do I apply Euler’s method to second order differential equations?

  • A?second order differential equation?is a differential equation containing one or more second derivatives
  • In this section of the course we consider second order differential equations of the formWorked Example5-7-2-ib-ai-hl-eulers-method-second-order-a-we-solution

5-7-2-ib-ai-hl-eulers-method-second-order-b-we-solution

 

Exact Solutions & Phase Portraits: Second Order

How can I find the exact solution for a second order differential equation?

  • In some cases we can apply methods we already know to find the exact solutions for second order differential equations
  • In this section of the course we consider second order differential equations of the form

How can I use phase portraits to investigate the solutions to second order differential equations?

  • Here we are again considering second order differential equations of the form

Worked Example5-7-2-ib-ai-hl-exact-second-order-a-we-solution

5-7-2-ib-ai-hl-exact-second-order-b-we-solution

5-7-2-ib-ai-hl-exact-second-order-c-we-solution

 

 

 

 

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