## Variable Coefficient Equations

How do you use variation parameters to find a general solution if you are given $y_1$ and $y_2$ are linearly independent. Where t>0

$

t^2y''-4ty'+6y=t^{3}+1
y_1 = 5t-1
y_2 = e^{-5t}
$

$

ty''+(1-2t)y' +(t-1)y = te^t
y_1 = e^t
y_2 = e^{t} ln t
$

Thanks CB for the LaTex lesson!!!