Inhomogeneous linear system of differential equation
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Find the solution to the given system that satisfies the initial condition
x'(t)= [0,2;4,-2]x(t) + [4t;-4t-2]
a) x(0)= [4;-5]
b) x(2)= [1;1]
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Solution Summary
Inhomogeneous linear system of differential equations are examined.
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Start from solving the homogeneous system:
x'(t)= [0,2;4,-2]x(t)
To solve is we find the eigenvalues: e_1 = -4 and e_2 = 2, and respective eigenvectors,
v_1 = [1;-2] and v_2 = [1;1] of the matrix [0,2;4,-2].
{ In case you need help in finding them: to find the eigenvalues solve the equation
det( [ 0-e, 2 ; 4, -2-e] ) = 0, and than find any vectors of arbitrary normalization which satisfy equations [ 0-e, 2 ; 4, -2-e] v = 0 }
Now, the ...
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