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sandrayuki
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1. Solve the following equation using the Method of Characteristics
xux +yuy=-u
subject to u(cos(s), sin(s)) = 1, 0 ≤ s ≤ pi
3. Characteristics for this equation are
dx/dt=x...(1)
dy/dt=y...(2)
du/dt=-u...(3)
From(3) get ln(u)=-t+c, u=k*exp(-t)
But i get stuck on the u(cos(s), sin(s)) = 1, i don't know how to use the initial contidion (u(cos(s), sin(s)) = 1 )to do the (1) and (2).
Can anyone help me to finish the rest of the question?
Many thanks
xux +yuy=-u
subject to u(cos(s), sin(s)) = 1, 0 ≤ s ≤ pi
Homework Equations
3. Characteristics for this equation are
dx/dt=x...(1)
dy/dt=y...(2)
du/dt=-u...(3)
From(3) get ln(u)=-t+c, u=k*exp(-t)
But i get stuck on the u(cos(s), sin(s)) = 1, i don't know how to use the initial contidion (u(cos(s), sin(s)) = 1 )to do the (1) and (2).
Can anyone help me to finish the rest of the question?
Many thanks
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