In each of Problems $1$ through $6,$ determine intervals in which solutions are sure to exist.

$y^{(4)}+4y^{\text{'}\text{'}\text{'}}+3y=t$

$t{y}^{\text{'}\text{'}\text{'}}+(sint)y^{\text{'}\text{'}}+3y=cost$

$t(t-1)y^{(4)}+e^t{y}^{\text{'}\text{'}}+4t^{2}y=0$

$y^{\text{'}\text{'}\text{'}}+t{y}^{\text{'}\text{'}}+t^2{y}^{\text{'}}+t^{3}y=lnt$

$(x-1)y^{(4)}+(x+1)y^{\text{'}\text{'}}+(tanx)y=0$

$(x^2-4)y^{(6)}+{}^2{y}^{\text{'}\text{'}\text{'}}+9y=0$

Question $4$ please