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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A: According to the given information, Consider the given integer n:

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A: #Answer of 2(e)

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A: we have to find laplace transform of t4

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Q: 3. Find the general solution of the partial differential equation *** (x" + y" )z ; m, ne IR* . ây

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Q: L-1 2s s2-10s+34) 34}

A: L-12ss2-10s+34

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A: The points are (1/4,1/2) and (1,1) the detailed solution is given below

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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.