A) \[y=c{{e}^{-{{x}^{2}}/2}}\]
B) \[y=c{{e}^{{{x}^{2}}/2}}\]
C) \[y=(x+c){{e}^{-{{x}^{2}}/2}}\]
D) None of these
Correct Answer: D
Solution :
[d] \[\frac{dy}{dx}=1+xy\] Or \[\frac{dy}{dx}-xy=1\] I.F. \[={{e}^{\int{-xdx}}}={{e}^{-{{x}^{2}}/2}}\] Hence solutions is \[y.{{e}^{-{{x}^{2}}/2}}=\int{{{e}^{-{{x}^{2}}/2}}dx+c.}\] \[\int{{{e}^{-{{x}^{2/2}}}}dx}\] is not further integrable.You need to login to perform this action.
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