Determine the second order equation

Question

Problem:Second order equation

1. Write the given second order equation as its equivalent system of first order equations.

uⁿ+8u′+2u=0

Use to represent the "velocity function", i.e. . ^u=u′(t)

Use v and u for the two functions, rather than ^u(t) and ^v(t). (The latter confuses webwork. Functions like are ^sin(t) ok.)

u′ =

v′ =

2. Write the given second order equation as its equivalent system of first order equations.

uⁿ-3u′+4u=-2sin(3t),  u(1)=4.5,   u′(1)=6

Use to represent the "velocity function", i.e. . ^u=u′(t)

Use v and u for the two functions, rather than ^u(t) and ^v(t). (The latter confuses webwork. Functions like are ^sin(t) ok.)

u′ =

v′ =