It's seems like a really simple question, but I can't understand how to solve it.
I am requested to decide which function $y=t^2$, or $y=t^2+1$ can be used for a particular solution of an order two equation: $y''+a(t)y'+b(t)y=0$ with the continues coefficients in all $\mathbb R$. I need to give the equation as well.
What should I do? usually I am asked to decide between two pairs, so I put each pair in it's Wronskian matrix and check if it's determinant can't be $o$ in all the given range. here $y=t^2+1$ is not $0$, but shouldn't I check its derive? and then usually I put both the pair and $y$ in a Wronskian matrix and find the equation, what should I do here?