Differential Equation system and matrix

Tala.S
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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 :
 

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yes, it is
 
That looks OK, assuming "v1" and "vf" are the same thing.
 
yes v1 = vf and v2 = 0
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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