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## Main Question or Discussion Point

[itex]y''(t) - \frac{2}{t^2}y(t) = 3 - \frac{1}{t^2}[/itex]

In this problem I had to solve two ways: Variation of Parameters and Undetermined Coefficients. I solved it using Variation of Parameters and got the correct answer for the particular solution in the back of the book being [itex]y_p(t) = t^2ln|t| + \frac{1}{2}[/itex]

I can't seem to get the same answer when I'm solving using Undetermined Coefficients. I let my assumption be [itex]y_p(t) = At^2 + Bt + C[/itex] but I only end up with [itex]C=\frac{1}{2}[/itex] while [itex]A=0[/itex] and [itex]B=0[/itex] when I go back and substitute into the original to find their values. What am I doing wrong here? Is my assumption incorrect? I somehow have to get a [itex]ln|t|[/itex] to match up with a [itex]t^2[/itex] as an A value then I should be able to get the same particular solution.

In this problem I had to solve two ways: Variation of Parameters and Undetermined Coefficients. I solved it using Variation of Parameters and got the correct answer for the particular solution in the back of the book being [itex]y_p(t) = t^2ln|t| + \frac{1}{2}[/itex]

I can't seem to get the same answer when I'm solving using Undetermined Coefficients. I let my assumption be [itex]y_p(t) = At^2 + Bt + C[/itex] but I only end up with [itex]C=\frac{1}{2}[/itex] while [itex]A=0[/itex] and [itex]B=0[/itex] when I go back and substitute into the original to find their values. What am I doing wrong here? Is my assumption incorrect? I somehow have to get a [itex]ln|t|[/itex] to match up with a [itex]t^2[/itex] as an A value then I should be able to get the same particular solution.