已知函数y=f(x)满足y″+2y′+5y=0,且f(0)=1,f′(0)=﹣1. 设

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问题 已知函数y=f(x)满足y″+2y′+5y=0,且f(0)=1,f′(0)=﹣1.

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答案∫f(x)dx=∫e-xcos2xdx   =﹣∫cos2xde-x=﹣cos2x·e-x+∫e-xdcos2x   =﹣excos2x+2∫e-xsin2xdx   =﹣excos2x+2sin2xe-x-4∫e-xcos2xdx,  [*]

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