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Solve-the-following-integral-equation-for-f-x-0-x-f-t-dt-3f-x-k-where-k-is-a-constant-




Question Number 1088 by 112358 last updated on 10/Jun/15
Solve the following integral  equation for f(x):  ∫_0 ^( x) f(t)dt=3f(x)+k  where k is a constant.
Solvethefollowingintegralequationforf(x):0xf(t)dt=3f(x)+kwherekisaconstant.
Answered by prakash jain last updated on 10/Jun/15
f(x)=3f ′(x)  f(x)=c e^(x/3)   ∫_0 ^( x) f(t)dt=c∫_0 ^( x) e^(t/3) dt=3ce^(x/3) −3c=3ce^(x/3) +k  ⇒c=−(k/3)  f(x)=−(k/3)e^(x/3)
f(x)=3f(x)f(x)=cex/30xf(t)dt=c0xet/3dt=3cex/33c=3cex/3+kc=k3f(x)=k3ex/3
Commented by 112358 last updated on 11/Jun/15
thanks
thanks

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