Compute the value of the constant k for which kx²e5x is a particular solution of the differential equation -10% + +25y = 6ex dx² Hence, solve the general solution of this differential equation.

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Q: Determine the curl and divergence of F(XYZ) = xye* ^-x³yze²^ + + xy²e¹ k

A: To find- Determine the curl and divergence of Fx, y, z = xyex i^ - x3yzez j^ + xy2ey k^.

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A: Given- Let y = 16 and u = 5-7.  To find- Write y as the sum of two orthogonal vectors, one in Span u…