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JEE Main & Advanced Mathematics Differential Equations Question Bank Linear defferential equations

  • question_answer
    The solution of differential equation \[\frac{dy}{dx}+y=1\] is [Pb. CET 2000]

    A)                 \[y=1+c\,{{e}^{-x}}\]      

    B)                 \[y=1-c\,{{e}^{-x}}\]

    C)                 \[y=x+c\,{{e}^{-x}}\]       

    D)                 \[y=x-c\,{{e}^{-x}}\]

    Correct Answer: A

    Solution :

                       \[\frac{dy}{dx}+y=1\]; I.F. \[={{e}^{\int{Pdx}}}={{e}^{\int{dx}}}={{e}^{x}}\]                    Hence solution is \[y.{{e}^{x}}=\int{{{e}^{x}}dx+c}\]                                 \[y{{e}^{x}}={{e}^{x}}+c\] Þ \[y=1+c{{e}^{-x}}\].


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