Explanation Given: The given equation is, ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r + 1 r 2 ∂ 2 u ∂ θ 2 = 0 With u ( r , θ ) = R ( r ) θ ( θ ) Calculation: Consider the given equation. ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r + 1 r 2 ∂ 2 u ∂ θ 2 = 0 … ( 1 ) Consider the equation. u ( r , θ ) = R ( r ) θ ( θ ) ... ( 2 ) Differentiate Equation (2) partially with respect to r . ∂ u ∂ r = R ′ ( r ) θ ( θ ) … ( 3 ) Differentiate Equation (3) partially with respect to r . ∂ 2 u ∂ r 2 = R ″ ( r ) θ ( θ ) Differentiate Equation (2) partially with respect to θ . ∂ u ∂ θ = R ( r ) θ ′ ( θ ) … ( 4 ) Differentiate Equation (4) partially with respect to θ . ∂ 2 u ∂ θ 2 = R ( r ) θ ″ ( θ ) Substitute R ( r ) θ ″ ( θ ) for ∂ 2 u ∂ θ 2 , R ″ ( r ) θ ( θ ) for ∂ 2 u ∂ r 2 and R ′ ( r ) θ ( θ ) for ∂ u ∂ r in Equation (1)

Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137394524

Author: R. Nagle, Edward Saff

Publisher: PEARSON+

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Chapter 10.2, Problem 27E

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The proof that solution that satisfy the indicated set of ordinary differential equation.

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Chapter 10.2, Problem 26E

Chapter 10.2, Problem 28E

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Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 6E Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...

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The proof that solution that satisfy the indicated set of ordinary differential equation.

Solution Summary: The author explains how to determine the proof that solves the indicated set of ordinary differential equations.

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The proof that solution that satisfy the indicated set of ordinary differential equation.

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