Consider the differential equation бу" + 7у" + 5у' — 8у %3D 4u" + би' — Зи Find the input matrix of the state-space representation of this differential equation.
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- Suppose that all the eigenvalues of the matrix A have negative real part. Then everysolution of the differential equation x`= Ax satisfies,|x(t)| ≤ |x(s)|, if t > s.solve the following system of linear non-homogeneous differential equations with eigenvalues/eigenvectors and variation of parametersWhat is the resulting differential equation after the initial substitution from the appropriate 2nd order transformation? Do not transpose terms to the other side of the equation. Continue from the solution obtained with the appropriate 2nd order transformation. If x = 4, C1 = -1/2, and C2 = 0, what is one possible value of y?
- Write the system of differential equations given in the 1st photo in the normal form defined in the 2nd photo and solve the resulting system by means of the eigenvalues and eigen-vectors of the square matrix A.Consider the system of differential equation x1'=t8x1+9sin(t)x2x1′=t8x1+9sin(t)x2 x2'=e4tx1+t5x2x2′=e4tx1+t5x2 Write the system in matrix form→x'=A→xx→′=Ax→ A=A=What is the resulting differential equation after the initial substitution from the appropriate 2nd order transformation? Do not transpose terms to the other side of the equation. Continue from the solution obtained with the appropriate 2nd order transformation. If x = 3, C1 = 0, and C2 = 0, what is the value of y?
- Convert the differential equation x'''=x''−2x'−4x+tx′′′=x′′-2x′-4x+t into a system of first order equations by letting u1=x,u2=x',u3=x''u1=x,u2=x′,u3=x′′Note: Type u_1, u_2, u_3, and t to write your variables.u1'u1′ = u2'u2′ = u3'u3′ = Submit QuestionQuestion 3Give a counter example of a symmetric matrix that all eigenvalues are negative real part but every solution of differential equation x`=Ax satisfies |x(t)|<|x(s)| if t>s.Determine the solution of the system of differential equations where a, b belong to R- [0]
- Find the general solution of the following system of differential equation. ThanksShow that the set of solutions of a second-order linear homogeneous differential equation is linearly independent.{eax, xeax}Write the system of differential equations given in the question in the normal form defined as in the 3rd photo and solve the resulting system through the eigenvalues and eigen-vectors of the square matrix A.