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JEE Main & Advanced Mathematics Differential Equations Question Bank Formation of differential equations

  • question_answer
    The differential equation found by the elimination of the arbitrary constant K from the equation \[y=(x+K){{e}^{-x}}\]is

    A)                 \[\frac{dy}{dx}-y={{e}^{-x}}\]       

    B)                 \[\frac{dy}{dx}-y{{e}^{x}}=1\]

    C)                 \[\frac{dy}{dx}+y{{e}^{x}}=1\]    

    D)                 \[\frac{dy}{dx}+y={{e}^{-x}}\]

    Correct Answer: D

    Solution :

                       \[y=(x+K){{e}^{-x}}\] Þ \[\frac{dy}{dx}=-(x+K){{e}^{-x}}+{{e}^{-x}}\]                                 Þ \[\frac{dy}{dx}=-y+{{e}^{-x}}\] Þ \[\frac{dy}{dx}+y={{e}^{-x}}\].


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