In Problems 25 – 28, use the elimination method to find a general solution for the given system of three equations in the three unknown functions x(t), y(t), z(t)
The solutions for the given linear system are , and .
Elimination Procedure for 2 × 2 Systems:
To find a general solution for the system
Where and are polynomials in :
Let us rewrite the given system of equations into operator form.
Multiply D-4 on equation (6). Then, substitute equation (4) and (5).
Since, the auxiliary equation to the corresponding homogeneous equation is:
. The roots are r =0 and r = 8.
Then, the general solution of z is
Now substitute equation (8) in equation (5).
So, the complementary solution of the differential equation is
Let us assume that function:
Find the derivation of equation (11).
Use the derivation in equations (9) to get,
Now, equalise the like terms.
Now substitute the equation (8) and (12) in equation (6)
So, the solution is founded.
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