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Sec 4.3: Homog DE (with constant Coefficients)

Sec 4.3: Homog DE (with constant Coefficients). Consider the second order linear DE. Find the Auxiliary equation of:. Find 2-Lin. Indep. Solutions:. HOW ??. Method (2ed order DE with constant coeff ). Given a homg DE:. Step 1. Find the Auxiliary equation:. Step 2. Find roots.

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Sec 4.3: Homog DE (with constant Coefficients)

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  1. Sec 4.3: Homog DE (with constant Coefficients) Consider the second order linear DE Find the Auxiliary equation of: Find 2-Lin. Indep. Solutions:

  2. HOW ?? Method (2ed order DE with constant coeff) Given a homg DE: Step 1 Find the Auxiliary equation: Step 2 Find roots (distinct real) Step 3 Two Linearly Independent Solutions are: Find 2-Lin. Indep. Solutions: Find 2-Lin. Indep. Solutions:

  3. Method (2ed order DE with constant coeff) Given a homg DE: Step 1 Find the Auxiliary equation: Step 2 Find roots Step 3 Three Cases: 2-distict real roots 2-repeated real roots 2- non-real roots Find 2-Lin. Indep. Solutions:

  4. WHY??? Euler’s Formula Find the following:

  5. Two Special Differential Equations Consider the second order linear DE Consider the second order linear DE

  6. Method (Higher order DE with constant coeff) Given a homg DE: Step 1 Find the Auxiliary equation: Step 2 Find roots Step 3 We have combination of Four Cases: distict real roots : (r-times) repeated real roots: Conjugate non-real: repeated Conjugate non-real: (r-times) Solve:

  7. Given that Is the general solution for a differential equation. Find this differential equation. Given that Is a solution to a homog DE with constant coeff Find a possible differential operator

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