II) Consider the following three equations ry-2w=0 y-2w² <-2 <<=0 5 <=0 1. Determine the total differential of the system. 2. Represent the total differential of the system in matrix form JV=Udz, where J is the Jacobian matrix, V = (dr dy dw)' and U a vector. 3. Are the conditions of the implicit function theorem satisfied at the point (x, y, w; 2) = (1,4,1,2)? Justify your answer. w² +2²-

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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II) Consider the following three equations
ry-2w = 0
y-2w². <-2 <=0
5
w² +2²-22w <=0
1. Determine the total differential of the system.
2. Represent the total differential of the system in matrix form
JV = Udz,
where J is the Jacobian matrix, V = (dr dy dw) and U a vector.
3. Are the conditions of the implicit function theorem satisfied at the
point (r, y, w: 2) = (1,4,1,2)? Justify your answer.
4. Using the Cramer's rule, find the expressions of , and at
(x, y, w; 2) = (1,4, 1,2).
Transcribed Image Text:II) Consider the following three equations ry-2w = 0 y-2w². <-2 <=0 5 w² +2²-22w <=0 1. Determine the total differential of the system. 2. Represent the total differential of the system in matrix form JV = Udz, where J is the Jacobian matrix, V = (dr dy dw) and U a vector. 3. Are the conditions of the implicit function theorem satisfied at the point (r, y, w: 2) = (1,4,1,2)? Justify your answer. 4. Using the Cramer's rule, find the expressions of , and at (x, y, w; 2) = (1,4, 1,2).
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