H$.$W solve the LVP:

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

$y(1)=1,y^{\text{'}}(1)=1$

H$.$w:

Let $f(t)=cosbt$

Find $L(f)$

H$.$w

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

HW: Show that:

given that $y_1(t)=\frac{1}{t}$

$f(t^n)=\frac{n^n}{s^{n+1},},n=0,1,2,$cdots,$s>0$

is the solution of the bongistous equation

H$.$w

find da greeal solution of

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