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Today's calculation of Integral 543

Source: 1970 Waseda University entrance exam/Science and Technology

January 31, 2010
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Let y y be the function of x x satisfying the differential equation y'' \minus{} y \equal{} 2\sin x. (1) Let y \equal{} e^xu \minus{} \sin x, find the differential equation with which the function u u with respect to x x satisfies. (2) If y(0) \equal{} 3,\ y'(0) \equal{} 0, then determine y y.
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