What Is the Laplace Transform Formula for \(\mathcal{L}[f(t) \cdot g'(t)]\)?

HWGXX7
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Hello,

I'am looking for de correct transformation formule:\mathcal{L}[f(t).g'(t)]
(and proof).

I'am not looking for method to solve it by means of integrating g'(t), offcourse this a possible way. But assume that g(t) is much work to calculate.

So is there a good one to one formule for it?

ty&grtz
 
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Anyone an idea?

ty
 
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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