In and 40, verify that the function defined by the definite integral is a particular
Chapter 1, Problem 39(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:
\(\frac{d}{d x} \int_{u(x)}^{v(x)} F(x, t) d t=F(x, v(x)) \frac{d v}{d x}-F(x, u(x)) \frac{d u}{d x}+\int_{u(x)}^{v(x)} \frac{\partial}{\partial x} F(x, t) d t\).
\(y^{\prime \prime}+9 y=f(x)\); \(y(x)=\frac{1}{3} \int_{0}^{x} f(t) \sin 3(x-t) d t\)
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