In$-$Class Work:

Solve the following ODEs using method of characteristic equations. If there are initial conditions, solve for the particular solution.

$($a$)y^{\text{'}\text{'}}-6y^{\text{'}}9y=0$

$($b$)y^{\text{'}\text{'}}-2y^{\text{'}}10y=0$

$($c$)2y^{\text{'}\text{'}}2y^{\text{'}}-y=0$

$($d$)y^{\text{'}\text{'}}14y^{\text{'}}49y=0,y(-4)=-1,y^{\text{'}}(-4)=5$

$($e$)9y^{\text{'}\text{'}}-12y^{\text{'}}4y=0,y(0)=2,y^{\text{'}}(0)=-1$

$($f$)y^{\text{'}\text{'}}4y^{\text{'}}4y=0,y(-1)=2,y^{\text{'}}(-1)=1$