Show that y1 = sin x² and y2 = cos x² are linearly in- dependent functions, but that their Wronskian vanishes at x = 0. Why does this imply that there is no differential equation of the form y" + p(x)y' + q(x)y = 0, with both p and q continuous everywhere, having both y1 and y2 as solutions?

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Q: Q1) Solve the following partial differential equation Ux + Uy = (cos x + sin y). U

A: 0

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