Q: What is the initial value if d²y/dx² + 4(dy/dx) + 3y = e⁻ˣ, with y(0) = 2, (dy/dx)|_{x=0} = 1?
(a)y(x) = (13/4 + x/2)e⁻ˣ − (5/4)e⁻³ˣ
(b)y(x) = (13/4 + x/2)e⁻³ˣ − (5/4)e⁻ˣ
(c)y(x) = (13/4 + x/2)e⁻ˣ + (5/4)e⁻³ˣ
(d)y(x) = (13/4 − x/2)e⁻ˣ − (5/4)e⁻³ˣ
Correct Answer: (a)
Detailed explanation coming soon.