Problems to Chapter 1. Differentiation rules Check whether the given functions are solutions of the corresponding...

 

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Problems to Chapter 1. Differentiation rules Check whether the given functions are solutions of the corresponding equa- tions. 1. y = (C₁ cos x + C₂ sin x)e-³/6, 2. u = F + y" + x²y + ²(x² + 4x + 4)y = 0 3. u= F(x+2y) + H (x+y), 5. u = F (2²y, ²) + x, 2uxx Ju əx X- du əx 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 = (C₁x + C₂)e(), where p(x) = du = 0 dy Ju +2 <=0 əz 1 11 rarctan r 1 [(a (arctan r)? + 2 1+x² In(x² + y=0 Problems to Chapter 1. Differentiation rules Check whether the given functions are solutions of the corresponding equa- tions. 1. y = (C₁ cos x + C₂ sin x)e-³/6, 2. u = F + y" + x²y + ²(x² + 4x + 4)y = 0 3. u= F(x+2y) + H (x+y), 5. u = F (2²y, ²) + x, 2uxx Ju əx X- du əx 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 = (C₁x + C₂)e(), where p(x) = du = 0 dy Ju +2 <=0 əz 1 11 rarctan r 1 [(a (arctan r)? + 2 1+x² In(x² + y=0

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1 y C1 cos x C2 sin x e x 2 2 To check if this function is a solution of the equation we need to sub... View the full answer