Consider the second order differential equation with initial conditions u^('')-4u^(') 4u=-4sin(3t),u(1)=-5.5,u^(')(1)=-4 Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the single letter v to represent the "velocity function"

Question

Consider the second order differential equation with initial conditions

u^('')-4u^(') 4u=-4sin(3t),u(1)=-5.5,u^(')(1)=-4

Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter

u

to represent the function

u

and the single letter

v

to represent the "velocity function"

u^(')

. Do not use

u(t)

or

v(t)

to represent these functions. Expressions like

sin(t)

that represent other functions are OK.

u^(')=
v^(')=

Now write the first order system using matrices:

(d)/(dt)[[u],[v]]=[[u],[v]] []

The initial value of the vector valued solution for this system is:

[[u(1)],[v(1)]]=[]

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(Solved): Consider the second order differential equation with initial conditions u^('')-4u^(') 4u=-4sin(3t),u ...