Suppose y1′ = t5y1 + 4y2 + sec(t), y2′ = sin(t)y1 + ty2 − 2. This system of linear differential equations can be put in the form y′ = P(t)y + g(t). Determine P(t) and g(t). P(t) = [ ] g(t) = [ ]
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Suppose
This system of linear differential equations can be put in the form . Determine and .
![Suppose y1′ = t5y1 + 4y2 + sec(t), y2′ = sin(t)y1 + ty2 − 2. This system of linear differential equations can be put in the form y′ = P(t)y + g(t). Determine P(t) and g(t). P(t) = [ ] g(t) = [ ]](https://www.doubtrix.com/uploads/editor/9028231548VLOvEsEeVB.png)
![Consider the system of differential equations y1′ = 28y1 − 14y2, y2′ = 35y1 − 14y2. a. Rewrite this system as a matrix equation y→′ = Ay→. y→′ = [ ]y→ b. Compute the eigenvalues of the coefficient matrix A and enter them as a comma separated list.](https://www.doubtrix.com/uploads/editor/3142793302RLrAqIlcLN.png)
![Suppose that the matrix A has the following eigenvalues and eigenvectors: λ1 = 1 with v→1 = [1 0]. and λ2 = −1 with v→2 = [4 1]. Write the solution to the linear system r→′ = Ar→ in the following forms. A. In eigenvalue/eigenvector form: [x(t) y(t)] = c1[ ]et + c2[ ]et B. In fundamental matrix form: [x(t)y(t)] = [ ][c1 c2] C. As two equations: (write "c1" and "c2" for c1 and c2 ) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 4v→1 or −3v→2.](https://www.doubtrix.com/uploads/editor/2097591975WwjdwwDMAQ.png)
![Suppose that the matrix A has the following eigenvalues and eigenvectors: λ1 = 1 with v→1 = [1 0]. and λ2 = −1 with v→2 = [4 1]. Write the solution to the linear system r→′ = Ar→ in the following forms. A. In eigenvalue/eigenvector form: [x(t) y(t)] = c1[ ]et + c2[ ]et B. In fundamental matrix form: [x(t)y(t)] = [ ][c1 c2] C. As two equations: (write "c1" and "c2" for c1 and c2 ) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 4v→1 or −3v→2.](https://www.doubtrix.com/uploads/editor/6708762412vXMQsPRlrb.png)
![Consider the linear system y→′ = [−3 −2 5 3]y→. a. Find the eigenvalues and eigenvectors for the coefficient matrix. λ1 = , v→1 = [ ], and λ2 = , v→2 = [ ] b. Find the real-valued solution to the initial value problem {y1′ = −3y1 − 2y2, y1(0) = −2 y2′ = 5y1 + 3y2, y2(0) = 5 Use t as the independent variable in your answers. y1(t) = y2(t) =](https://www.doubtrix.com/uploads/editor/6174151511mUCFTgrlOM.png)