Question 1 Using the definition of the exponential of a matrix compute elA where 0 1 0 A = |0 0 1 0 0 0 Use this exponential to solve the system of differential equations with initial con- ditions f(0) = 1, g(0) = 1, h(0) =1. df g(t) dt dg = h(t) dt dh = 0 dt %3D

Q: e general solution of the differential equation y(4) — 4y" = t² + et.

A: Given differential equation, y4 - 4y” = t2 + et   for complementary function consider auxiliary…

Q: y " – y = x²e*

A:

Q: x* + 2x – 4 3 x' + 3 x²

A: The solution are next step

Q: 8. xy" - xy + y = 0 y₁(x) = x

A:

Q: Title of Assignment: Engineering Applications of first order linear Differential Equations ( with…

A: To explain: First order linear differential equation with any two applications in engineering.

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: Describe the impact of duality on the understanding and analysis of linear differential equations

A: Duality plays a significant role in the understanding and analysis of linear differential equations,…

Q: 1. y-14y- 48y = 0 2. y'-12y + 27y = 0

A:

Q: (b) What is the differential equation satisfied by y(x)?

A: Just divide second differential equation by first differential equation.

Q: Which system of differential equations describes a situation where the two species compete and which…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (a). If you…

Q: Find the general solution of the differential equation.

A:

Q: Solve the differential equation (b and a are variables) (D2+4D+3)b=1+2a+3a2

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.