System of linear differential equations

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For a system of linear differential equations with constant coefficients with known initial conditions an analytical solution can be found.
I however have a system of linear differential equations, where the coefficients are timedependent with the dependence of the coefficients being α_n(t)=exp(k*n*t). Is such a system solvable in general? If I need to be more specific let me know and I will write down the exact system, but for now is there anything general to say?
 
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More of a technical question than homework, so I moved it to the Math technical sections.
 
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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