Second Order differential eqn with 2 solutions (pls help!)

[woshifate]

Suppose that two function y(t) and z(t) satisfy

dy/dt = -4y + 2z
dz/dt = -2y + 4t² + 4

and suppose that y(0)=1 and z(0) = 7/2. Find the functions y and z

 

[Ishuda]

Suppose that two function y(t) and z(t) satisfy

(1) dy/dt = -4y + 2z
(2) dz/dt = -2y + 4t² + 4

and suppose that y(0)=1 and z(0) = 7/2. Find the functions y and z

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
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As a hint I would probably start with differentiating (1) and then using (2) for the dz/dt.