Ordinary differential equations involving matrices

ricky786
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hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please

thanks
 

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Hi ricky786! Welcome to PF! :smile:
ricky786 said:
hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please

thanks

Hint: If the eigenvalues are -1 and ±i, then there's a basis in which x' = -x, y' = iy, z' = -iz …

now solve. :wink:​
 
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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