A) \[y=c{{e}^{x-{{x}^{2}}}}\]
B) \[y=c\,{{e}^{{{x}^{2}}-x}}\]
C) \[y=c\,{{e}^{x}}\]
D) \[y=c\,{{e}^{-{{x}^{2}}}}\]
Correct Answer: A
Solution :
[a] \[\frac{dy}{dx}+2xy=y\] Or \[\frac{dy}{dx}=y(1-2x)\] Or \[\frac{dy}{dx}=(1-2x)dx\] Or \[\log y=x-{{x}^{2}}+{{c}_{1}}\] Or \[y={{e}^{x-{{x}^{2}}}}{{e}^{{{c}_{1}}}}=c{{e}^{x-{{x}^{2}}}}\]where \[c={{e}^{{{c}_{1}}}}\] Thus, \[y=c{{e}^{x-{{x}^{2}}}}\]is the required solution.
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