Constructing A Differential Equation From A Solution Set

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The discussion focuses on constructing a differential equation from a given solution set, specifically y = c1e3xcos(2x) + c2e3xsin(2x) + c3 + c4x. There is uncertainty regarding the roots associated with the constants c3 and c4, with a suggestion that they represent a repeated root, potentially k = 0. Participants emphasize the importance of deriving the correct differential equation that aligns with the provided solution. Ultimately, confirming that the derived equation matches the solution set is critical to solving the problem. The conversation highlights the connection between the solution form and the corresponding differential equation.
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Homework Statement



y = c1e3xcos(2x)+c2e3xsin(2x)+c3+c4x


Homework Equations



Differential Equations.

The Attempt at a Solution


I am having trouble what the roots are for the c3, and c4 parts. I know they are a repeated root, but is it just k= 0? It seems like it would work, but I am not sure.
 
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Baumer8993 said:

Homework Statement



y = c1e3xcos(2x)+c2e3xsin(2x)+c3+c4x


Homework Equations



Differential Equations.

The Attempt at a Solution


I am having trouble what the roots are for the c3, and c4 parts. I know they are a repeated root, but is it just k= 0? It seems like it would work, but I am not sure.

You are on the right track. What is the differential equation you got? If the solution of it agrees with the given one, you solved the problem.

ehild
 
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