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JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The solution of the given differential equation \[\frac{dy}{dx}+2xy=y\] is [Roorkee 1995]

    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 :

    • \[\frac{dy}{dx}+(2x-1)y=0\]; I.F. \[={{e}^{\int_{{}}^{{}}{(2x-1)dx}}}={{e}^{{{x}^{2}}-x}}\]                   
    • Required solution is \[y{{e}^{{{x}^{2}}-x}}=c\]or\[y=c{{e}^{x-{{x}^{2}}}}\].


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