2OLE Variation of Parameters

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Main Question or Discussion Point

[tex]ty''-(t+1)y'+y=t^2[/tex]

I know I have to use variation of parameters to solve this.
But I am stuck and cannot figure out how to get the homologous equation!
[tex]y''-(1+\frac{1}{t})y'+\frac{1}{t}*y=t[/tex]

I don't know how to solve this homologous equation in this format.

Is it R^2+(1+1/t)R+1/t = 0 ?
How would I get my two solutions from this?

Thanks!
 
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[V]
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Whats wrong with the latex??
 
LCKurtz
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[V];3246347 said:
[tex]ty''-(t+1)y'+y=t^2[/tex]

I know I have to use variation of parameters to solve this.
But I am stuck and cannot figure out how to get the homologous equation!
[tex]y''-(1+\frac{1}{t})y'+\frac{1}{t}*y=t[/tex]

I don't know how to solve this homologous equation in this format.

Is it R^2+(1+1/t)R+1/t = 0 ?
How would I get my two solutions from this?

Thanks!
Your homogeneous equation is

[tex]ty''-(t+1)y'+y=0[/tex]

This equation has a regular singular point at t = 0 suggesting you look for series solutions of the form

[tex]y = \sum_{n=0}^{\infty}a_nt^{n+r}[/tex]
 

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