# General Solution of inhomogeneous ODE

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1. Jan 26, 2016

### Just_some_guy

I am having a little trouble with a problem I am trying to solve.

Given three particular solutions

Y1(x)= 1, Y2(x)= x and Y3(x)= x^2

Write down a general solution to the second order non homogeneous differential equation.

What I have done so far is to realise if Y1,2 and 3 are solutions then the difference of two of the solutions is a solution to the homogeneous equation. So I used Y3-Y1, Y3-Y2 and Y2-Y1 to give three separate homogeneous equations. At this point I am trying so solve for the coefficients a(x), b(x) and c(x) from

a(x)y'' + b(x)y' + c(x) y= 0

where y is the difference of two of the particular solutions.

However I can seem to solve this system effectively by equating like powers etc... I was hoping someone could offer some advise or even an alternative method. I have solved problems like this with only two solutions but the case was simple.

Regards
Guy

2. Jan 26, 2016

### Staff: Mentor

In future posts, please do not delete the homework template. Its use is required for homework questions.

3. Jan 26, 2016

### Just_some_guy

Apologies I didnt realise it was necessary