If , then prove that…

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

If y=∫0xf(t)sin⁡{K(x−t)} dty = \int_{0}^{x} f(t)\sin\{K(x-t)\}\,dt, then prove that d2ydx2+K2y=Kf(x)\frac{d^2y}{dx^2} + K^2y = Kf(x).

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