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JEE Main & Advanced Mathematics Differential Equations Question Bank Variable Separable type differential equations

  • question_answer
    The solution of the equation \[\frac{dy}{dx}=y({{e}^{x}}+1)\]is [AISSE 1986; AI CBSE 1984]

    A)                 \[y+{{e}^{({{e}^{x}}+x+c)}}=0\]            

    B)                 \[\log y={{e}^{x}}+x+c\]

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

    D)                 None of these

    Correct Answer: B

    Solution :

                       \[\frac{dy}{dx}=y({{e}^{x}}+1)\] Þ \[\frac{dy}{y}=({{e}^{x}}+1)dx\]                 Integrating both sides, we get \[\log y={{e}^{x}}+x+c\].


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