Differential Equation system and matrix

[Tala.S]

I have a quick question.
I have to write the differential equations in matrix form

Eq1:= x1'(t) = -a1*x1(t) + vf

Eq2:= x2'(t) = a1*x1(t) - a2*x2(t)

is this correct :

 

[guest1234]

yes, it is

 

[AlephZero]

That looks OK, assuming "v1" and "vf" are the same thing.

 

[Tala.S]

yes v1 = vf and v2 = 0

 

[blue_raver22]

The differential equations presented can be written in matrix form as:

x'(t) = Ax(t) + b

where x(t) is the vector [x1(t), x2(t)] and A is the matrix [-a1, 0; a1, -a2] with b = [vf, 0]. This matrix form allows for a more compact and efficient representation of the system of equations, making it easier to analyze and solve. It is a common approach in mathematics and physics to use matrices to represent systems of differential equations.