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

  • question_answer
    The solution of \[{{e}^{2x-3y}}dx+{{e}^{2y-3x}}dy=0\] is

    A)                 \[{{e}^{5x}}+{{e}^{5y}}=c\]     

    B)                 \[{{e}^{5x}}-{{e}^{5y}}=c\]

    C)                 \[{{e}^{5x+5y}}=c\]       

    D)                 None of these

    Correct Answer: A

    Solution :

                       \[{{e}^{2x-3y}}dx+{{e}^{2y-3x}}dy=0\]         Multiply the equation by \[{{e}^{3x+3y}}\]Þ \[{{e}^{5x}}dx+{{e}^{5y}}dy=0\]                 On integrating, we get \[{{e}^{5x}}+{{e}^{5y}}=5c'=c\].


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