Laplace Transform Integration: Tips & Solutions

lostinhere
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This question may be obvious but I am stumped. I know the definition of a Laplace Transform is integration of e^(-st)f(t). However, I don't know how to integrate with both s and t variables included. If anyone could provide insight I would appreciated it.
 
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The integration is only over the variable t and you treat s as a constant.
 
thanks, I knew it was simple
 
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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