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M5 Help!!!!

Just finished M4(phew) and now starting M5.I have started differential equations involving vectors.Despite being able to solve the questions with relative ease, I dont actually understand whats going in.Could somebody enlighten me as to why intergrating with respect to a vector is undefined?(as the book describes it)
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mik1a
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What would it mean? Integrating with respect to a vector?
Original post by mik1a
What would it mean? Integrating with respect to a vector?

I initially thought we would just treat it as a scalar, kind of how problems were treated in the earliest mechanics modules that why Im confused.What im asking probably does seem a little bit silly for someone learning m5, but my maths teachers cant really help me as they cant even do m5 themselves
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mik1a
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I'm just not sure what the question is. Why can't you integrate with respect to a vector? Like dy/d(x,y)? Is that what you're asking?

When you say treat 'it' as a scalar, treat what?
Original post by mik1a
I'm just not sure what the question is. Why can't you integrate with respect to a vector? Like dy/d(x,y)? Is that what you're asking?

When you say treat 'it' as a scalar, treat what?

The question is dv/dt=4v, where v is a velocity vector.Now i thought it could be solved by seperating the variable,however you cant do that according to the book because it is undefined.Instead the complemenaty functiob has to be found by setting the eqyation equal to zero.
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mik1a
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There's a lack of information and precision here. What is the exact question? Solve a differential equation dv/dt = 4v?
Original post by mik1a
There's a lack of information and precision here. What is the exact question? Solve a differential equation dv/dt = 4v?

A particle P is moving in a plane such that at time t seconds its position vector is r metres a and its velocity is vms^-1Hiven that v statisfies the differential equation dv/dt=4v and that t=0,r=2i-j and v=i+3j, find an expession for r in terms of t.
I can solve it, but instinctley I would solve it by seperating the variable in dv/dt=4t, but the official book says that intergrating a vector like this is undefined, so I found the general soultion and the complementary function from the intial conditions.Although i got the correct answer, I dont understand why I couldn't seperate the variable in the first place

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