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Exercise 3.1.4. The set of all twice differentiable functions f for which f"(x) +2f(x) = 0 holds.

Exercise 3.1.4. The set of all twice differentiable functions f for which f"(x) +2f(x) = 0 holds.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve only 3.1.4.    Exercise

In the first ten exercises determine whether the given set describes a vector space or not. For each function space the operations are defined by Equa- tions 3.1 and 3.2. Explain your answers! Exercise 3.1.1. The set of all polynomials of degree two and the zero poly- nomial. Exercise 3.1.2. The set of all solutions (x, y) of the equation 2x + 3y = 0, with addition and multiplication by scalars defined as in R². Exercise 3.1.3. The set of all solutions (x, y) of the equation 2x + 3y = 1, with addition and multiplication by scalars defined as in R². Exercise 3.1.4. The set of all twice differentiable functions f for which f"(x) +2f(x) = 0 holds.
Transcribed Image Text:In the first ten exercises determine whether the given set describes a vector space or not. For each function space the operations are defined by Equa- tions 3.1 and 3.2. Explain your answers! Exercise 3.1.1. The set of all polynomials of degree two and the zero poly- nomial. Exercise 3.1.2. The set of all solutions (x, y) of the equation 2x + 3y = 0, with addition and multiplication by scalars defined as in R². Exercise 3.1.3. The set of all solutions (x, y) of the equation 2x + 3y = 1, with addition and multiplication by scalars defined as in R². Exercise 3.1.4. The set of all twice differentiable functions f for which f"(x) +2f(x) = 0 holds.
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