Math Help - Using maple to solve a an equation where one solution is known

1. Using maple to solve a an equation where one solution is known

What command would I use to ask maple to solve the following

$x''=\frac{t+1}{t}x'-\frac{1}{t}x$

with $x_1(t)=e^t$

I know about the dsolve command but I'm not sure how to tell it what the other solution is.

2. Here is a screenshot of the maple commands.

maple.pdf

Now use set

$c_1=0\quad c_2=1$

this gives

$u(t)=(t+1)e^{-t}$

$y=u(t)e^{t}=(t+1)e^{-t}e^{t}=t+1$

So this is the other linearly independent solution.