Answer:
Step-by-step explanation:
DE given is
y''+8y'+15y=0, y(0)=0, y'(0)=1
Take Laplace on the DE
We get

Simplify to get
Y(s) = ![\frac{1}{2}[ {\frac{1}{s+3} -\frac{1}{s+5} }]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%20%7B%5Cfrac%7B1%7D%7Bs%2B3%7D%20-%5Cfrac%7B1%7D%7Bs%2B5%7D%20%7D%5D)
Take inverse

Answer:
x= 1 or x= 1.56 (3 s.f.) or x= -2.56 (3 s.f.)
Step-by-step explanation:
Please see attached picture for full solution.