I have a diff. equation given as;

What is the general solution

to the assosiated diff. equation? (Thinking)

Any help/pointers would be greatly appriciated!

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- November 6th 2008, 12:17 PMjokke22Differential equation
I have a diff. equation given as;

What is the general solution

to the assosiated diff. equation? (Thinking)

Any help/pointers would be greatly appriciated! - July 17th 2016, 05:51 AMRebesquesRe: Differential equation
This is in fact the discrete analogue to a differential equation, called a difference equation.

Begin by searching for solutions to the associated homogeneous equation:

Set and substitute to obtain the quadratic , with solutions

.

The general solution to the homogeneous equation becomes , where the are constants.

Now we seek for a particular solution to the original equation. Since the right hand side is a quadratic polynomial in , we can try where are to be determined by substitution.

After this is done, the general solution to the original equation is .