In: Advanced Math
Please show work! I have the answers to these parts, but I am having trouble working through the problem to find the answer.
Find the solution of the IVP:
d.) 5y" - y' = 0, y(0) = -1, y'(0) = -1 (answer: y(t)=4 - 5 et/5)
e.) 3y" - y = 0, y(0) = 3, y(t) is bounded for 0 <= t < infinity (answer: y = 3 exp(-(1/3)sqrt(3)t) )
g.) y" + 2y' + y = 0, y(0) = -1, y'(0) = 0 (answer: y(t) = - e-t - e-t t )
h.) y" + 9y = 0, y(0) = -1, y'(0) = -1 (answer: y(t) = -1/3 sin(3t) - cos(3t) )
i.) y" + 2y' + 5y = 0, y(0) = -1, y'(0) = -1 (answer: y(t) = -e-t sin(2t) - e-t cos(2t) )