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f-x-xf-x-f-x-




Question Number 6177 by FilupSmith last updated on 17/Jun/16
f ′(x)=xf(x)  f(x)=??
f(x)=xf(x)f(x)=??
Answered by Yozzii last updated on 17/Jun/16
(df/dx)=xf  ⇒∫(df/f)=∫xdx  ln∣f(x)∣=(x^2 /2)+C  f(x)=Ae^(x^2 /2)   (A=arbitrary constant)  f′(x)=xAe^(x^2 /2) =xf(x)
dfdx=xfdff=xdxlnf(x)∣=x22+Cf(x)=Aex2/2(A=arbitraryconstant)f(x)=xAex2/2=xf(x)

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