Determine all solutions u = u(x1, x2) of du du (1 — и). + (1+u) dx1 = 1, dx2 X1, X2 E R, u(x1, x2) = 0, xi = x2. Nhere are the solutions defined? Interpret your results in the light of the general local existence theorem.

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Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

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Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

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Q: Using an appropriate linearization, the local linear approximation of f(x)%3D+ cos r at is 2.

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A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.