设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0
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设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0设f(x)连
设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0
设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0
设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0
化积分方程为微分方程.两边同时对 x 求导:
f '(x) = sinx + f(x),即 f '(x) - f(x) = sinx
这是一阶线性方程,f(x) = C e^x + (sinx-cosx)/2
由原方程可以得到:f(0) = -1
于是,常数 C = -1/2
=> f(x) = (-1/2) e^x + (sinx-cosx)/2
设f(x)连续且满足f(x)=-cosx+∫f(t)dt,求f(x).注:积分上限为x下限为0
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