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Math · Calculus
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5a 3 First find the eigenvalues eigenvectors of the matrix A- 3 -2 The eigenvalues are λ1=1, λ2 1, with eigenvectors: vi V2= The solution of the homogeneous system: x(t) G | ¡ | et + C2 | | e-t 5b 1 u1(t 5c 3 Variation of parameters: start from xp(t)- F(t)u(t) Substitution in the (inhomogeneous) DE_common practice - yields F(t)u(t)-g(t), where g(t) denotes the inhomogeneous part For u(t) we have to solve the system with augmented matri:x let le-t e le 3e-t t 1 01 3-te-t 0 2e-t- e u1(t) Integrating gVeSu2(t) 2 and multiplying with the fundamental ives t12t 1 2 4t -5 matrix leads to xp(t)-F(t)u(t) -... - 46t - 3Let step says that the particular solution is u(t) multiplied by the fundamental matrix. Could you please give step by step of this part?

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