Ben cunnington
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- Joined
- Apr 17, 2016
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Consider the vector field F(x,y,z) = ax i + by j + cz k where F, i, j, k are vectors
Let c(t) = (x(t), y(t), z(t)) be the flow line such that c(0)= (x_0, y_0, z_0). Find c(t) for all t. Note: c is a vector and x_0 represents a constant, like those x's with the 0's on the bottom right hand corner.
I know that if c(t) is a flow line then c'(t) = F( c(t) ) but I have no idea what this question is actually asking for. Thanks in advance for any help/tips.
Edit: I think I'm supposed to solve the differential equation c'(t) but I'm at a dead end given that c(t) is actually given.
Edit: Sorry, again. I've added the "Find"
Let c(t) = (x(t), y(t), z(t)) be the flow line such that c(0)= (x_0, y_0, z_0). Find c(t) for all t. Note: c is a vector and x_0 represents a constant, like those x's with the 0's on the bottom right hand corner.
I know that if c(t) is a flow line then c'(t) = F( c(t) ) but I have no idea what this question is actually asking for. Thanks in advance for any help/tips.
Edit: I think I'm supposed to solve the differential equation c'(t) but I'm at a dead end given that c(t) is actually given.
Edit: Sorry, again. I've added the "Find"
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