Suppose $y=1$ and $y=xlnx$ are solutions to some second-order homogenous differential equation. Construct the equation.
Edit #1: OK, the Wronskian gives $lnx+1$ but I don't see how this helps me.
I assume you want a 2nd order homogeneous linear equation, which is to say, you want functions $a(x),b(x),c(x)$ such that $$a(x)y''+b(x)y'+c(x)y=0$$ identically. So, put in $y=1$, and you get an equation relating $a,b,c$. Put in $y=x\log x$, and you get another equation relating $a,b,c$. Now find $a,b,c$ satisfying those two equations.