2. 考研
  3. 设f(x)连续且f(x)≠0，又设f(x)满足f(x)=∫0xf(x—t)dt+∫01f2(t)dt，则f(x)= _________．

设f(x)连续且f(x)≠0，又设f(x)满足f(x)=∫0xf(x—t)dt+∫01f2(t)dt，则f(x)= _________．

admin2016-05-03  34
问题 设f(x)连续且f(x)≠0，又设f(x)满足f(x)=∫0xf(x—t)dt+∫01f2(t)dt，则f(x)= _________．
选项
答案[*]
解析 f(x)=∫0xf(x一t)dt+∫01f2(t)dt
    =一∫x0f(u)du+∫0xf(t)dt=∫0xd(u)du+∫01f(t)dt．
令∫01f2(t)dt=a，于是
    f(x)=∫0xf(u)du+a，f’(x)=f(x)，f(0)=a，
解得f(x)=cex．由f(0)=a，得f(x)=aex，代入∫01f2(t)dt=a中，得
转载请注明原文地址:https://kaotiyun.com/show/S1T4777K
0

考研数学三

相关试题推荐
随机试题
最新回复(0)