- Consider the initial-value problem t dr = te ^¹i + (₁2²+1) ³ dt 7(0) = i + 3j (a) Solve the initial-value problem. Show the steps of your process thoroughly.

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Q: Find the isogonal trajectories cutting at an angle of arctan 4 to the family of curves y = Inx + C.

A: Family of curves: y=lnx+C The isogonal trajectory cutting at an angle of tan-14

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A: We will use properties of integrals. In 1st problem we use substitution method .

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Q: 4. For the cylinder with patch (a) Find the normal vector U. (b) The Gauss X(u, v) = (R cos u, R sin…

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A: Following definition of orthogonal and orthonormal vectors, we find these solutions.

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