Using Laplace to solve a differential equation

sim907
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Use Laplace to solve x''+3x'+5x=sin(8t)
Initial conditions x(0)= 2 and x'= -3

I have worked it down to (s2+3s+5)X(s)= 2s+3+ [8/(s2+64)] but stuck. Please help
 
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sim907 said:
Use Laplace to solve x''+3x'+5x=sin(8t)
Initial conditions x(0)= 2 and x'= -3

I have worked it down to (s2+3s+5)X(s)= 2s+3+ [8/(s2+64)] but stuck. Please help

Try completing the square on (s2+3s+5)
 
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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