wen aeYAR ondition (6) implies alevector v (x0\'ye,.) is no tGgeMe to the curve

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wen aeYAR ondition (6) implies alevector v (x0'ye,.) is no tGgeMe to the curve C at the point (xoo). Example: Consider the quasi-linear equation Let the initial curve C be given by Find the solution z = z (x,y ) which on the initial curve C has the values First, we express the curve C in the parametric form as And on C the solution must take the values z 1 +1 In geometrical terms the problemis to find the solution surface =z(x,y) z Containing the curve C given by The vector field And on the curve C (2+1 ) )-(1-1 #0 dt d Thus, the condition (6) is satisfied at every point of C and we know that there exists a unique solution to the problem in the neighborhoodof every point of C The system of equations associated with the vector field Vis ytzy x-y Where we found the two first integrals r +2 These first integrals are defined and are functionally independent in the domain x-y0, y >0 which containsthe curve C. To find the integral surface of Vcontaining C we compute

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What's your question? Can you please ask precisely what do you want? Here I can find a problem with the solution. What do you expect from me?

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