Question

Let H: \(\R\rightarrow\R\) be the function given by H(x) = \(\frac{1}{2}(e^x+e^{-x})\) for \(x\isin\R\).
Let f: \(\R\rightarrow\R\) be defined by
\(f(x)=\displaystyle\int_{0}^{\pi}H(xsin\theta)d\theta\) for \(x\isin\R\)
Then which one of the following is true?

• A. xf"(x) + f'(x) +xf(x) = 0 for all \(x\isin\R\).
• B. xf"(x) + f'(x) +xf(x) = 0 for all \(x\isin\R\).
• C. xf"(x) + f'(x) +xf(x) = 0 for all \(x\isin\R\).
• D. xf"(x) + f'(x) +xf(x) = 0 for all \(x\isin\R\).

Answer 1

The Correct Option is C

The correct option is (C): xf"(x) + f'(x) +xf(x) = 0 for all \(x\isin\R\).