What are the steps for solving a 2nd order differential equation?

[wombat4000]

Homework Statement

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Homework Equations

The Attempt at a Solution

this isn't a straight forward calculate the soltion to a 2nd ode so I am pretty stumped.

 

[Defennder]

Firstly, suppose y1 is a solution to y''+ay'+by=g(x). What then is a solution of y''+ay'+by=kg(x), where k is an arbitrary non-zero constant?

Secondly, note that a general solution to a non-homogenous linear ODE is its homogenous solution plus one particular solution to its nonhomogenous ODE.

 

[wombat4000]

solution to y''+ay'+by=kg(x) is ky1?

so the solution to y''+ay'+by=3g(x) is the complimentyery function + particular integral = 3y1 + y2?

 

[Defennder]

That should be correct.

 

[wombat4000]

thanks!
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