Problems to Chapter 1. Differentiation rules Check whether the given functions are solutions of the corresponding equa- tions. 1. y = (C cos x + C sin x)e-/6, 2. u = F + y" + xy + (x + 4x + 4)y = 0 3. u= F(x+2y) + H (x+y), 5. u = F (2y, ) + x, 2uxx Ju x X- du x 2Uzz3uzy + Uyy = 0 1 - 4. u = F(x + 2y) + H (x + y) y(x + 2y)(x + y), 3uxy + Uyy = y + y" + y arctanz+ F 1 Ju y dy 247 6. y = (Cx + C)e(), where p(x) = du = 0 dy Ju +2