- #1
Just_some_guy
- 16
- 0
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 realize 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
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 realize 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
