In and 40, verify that the function defined by the definite integral is a particular
Chapter 1, Problem 40(choose chapter or problem)
In Problem 39 and 40, verify that the function defined by the definite integral is a particular solution of the given differential equation. In both problems, use Leibniz’s rule for the derivative of an integral:
\(\frac{d}{d x} \int_{u(x)}^{v(x)} F(x, t) d t=F(x, v(x)) \frac{d v}{d x}-F(x, u(x)) \frac{d u}{d x}+\int_{u(x)}^{v(x)} \frac{\partial}{\partial x} F(x, t) d t\).
\(x y^{\prime \prime}+y^{\prime}-x y=0\); \(y=\int_{0}^{\pi} e^{x \cos t} d t\) [Hint: After computing \(y^{\prime}\) use integration by parts with respect to t.]
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