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

  • question_answer
    If \[\frac{dy}{dx}={{e}^{-2y}}\] and \[y=0\] when \[x=5,\] the value of x for \[y=3\] is         [MP PET 2001]

    A)                 \[{{e}^{5}}\]      

    B)                 \[{{e}^{6}}+1\]

    C)                 \[\frac{{{e}^{6}}+9}{2}\]               

    D)                 \[{{\log }_{e}}6\]

    Correct Answer: C

    Solution :

                       \[\int_{{}}^{{}}{\frac{dy}{{{e}^{-2y}}}}=\int_{{}}^{{}}{dx}\] Þ \[\frac{{{e}^{2y}}}{2}=x+c\]                 At \[x=5,\ y=0\]Þ \[c=-\frac{9}{2}\]; \[\therefore \]For \[y=3,\ x=\frac{{{e}^{6}}+9}{2}\].


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