This week we will look at second order differential equations. Here are some que

Question

This week we will look at second order differential equations. Here are some questions we will address. Please post answers to these questions in this thread.

1.How is a second order differential equation different form a first order?

2.What clues does the notation give us?

3.How is a homogeneous differential equation different from a non-homogeneous differential equation?

4.What steps should we follow to solve a homogeneous differential equation?

5.What steps should we follow to solve a non-homogeneous differential equation?

6.How do we ensure that each term in the solution to a differential equation is unique?

Explanation / Answer

1. For a second order differential equation, the highest order of dy/dx is 2 whereas for first order differential equation it is 1.

2. A homogenous differential equation, doesn't have any constant x terms within it, whereas non-homogenous equation does have x term and constant term within it.

Example: dy/dx + ky = 0 is a homogenous equation where as dy/dx + ky = bx + c is a non-homogenous equation where k,b and c are constants.

3. Homogenous differential equation can solved by substituting approriate functions, generally y= Ae^kx

4. Non-homogenous differential  equations are solved using particular integral method.

5. All the solutions obtained by substitution method are taken as linear combination to represent the set of solutions for the differential equation.

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