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

  • question_answer
    The solution of \[\log \,\left( \frac{dy}{dx} \right)=ax+by\] is         [AMU 2002]

    A)                 \[\frac{{{e}^{by}}}{b}=\frac{{{e}^{ax}}}{a}+c\]   

    B)                 \[\frac{{{e}^{-by}}}{-b}=\frac{{{e}^{ax}}}{a}+c\]

    C)                 \[\frac{{{e}^{-by}}}{a}=\frac{{{e}^{ax}}}{b}+c\]  

    D)                 None of these

    Correct Answer: B

    Solution :

                       \[\log \left( \frac{dy}{dx} \right)=ax+by\] Þ \[\frac{dy}{dx}={{e}^{ax+by}}={{e}^{ax}}.{{e}^{by}}\]                                 Þ \[{{e}^{-by}}dy={{e}^{ax}}dx\] Þ \[\frac{{{e}^{-by}}}{-b}=\frac{{{e}^{ax}}}{a}+c\].


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