Answer
y=$\frac{1}{4}$$e^{t}$+$e^{-t}$
Work Step by Step
Roots of a characteristic equation:
$r^{2}$-1=0
$r^{2}$=1
r=±1
General solution:
y=$c_{1}$$e^{t}$+$c_{2}$$e^{-t}$
Initial conditions:
y(0)=$\frac{5}{4}$
$c_{1}$+$c_{2}$=$\frac{5}{4}$
$y^{1}$=$c_{1}$$e^{t}$-$c_{2}$$e^{-t}$
$y^{1}$(0)=-$\frac{3}{4}$
$c_{1}$-$c_{2}$=-$\frac{3}{4}$
$c_{1}$+$c_{2}$+$c_{1}$-$c_{2}$=$\frac{5}{4}$-$\frac{3}{4}$
$c_{1}$=$\frac{1}{4}$
$c_{2}$=1
