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JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The solution of the equation \[\frac{dy}{dx}=\frac{1}{x+y+1}\] is

    A) \[x=c{{e}^{y}}-y-2\]           

    B) \[y=x+c{{e}^{y}}-2\]

    C) \[x+c{{e}^{y}}-y-2=0\]      

    D) None of these

    Correct Answer: A

    Solution :

    • \[\frac{dy}{dx}=\frac{1}{x+y+1}\]Þ \[\frac{dx}{dy}=x+y+1\]Þ\[\frac{dx}{dy}-x=y+1\]        
    • It is linear equation, therefore I.F. \[={{e}^{\int_{{}}^{{}}{-1dy}}}={{e}^{-y}}\]        
    • Hence the solution of the equation is           
    • \[x.{{e}^{-y}}=\int_{{}}^{{}}{(y+1){{e}^{-y}}}dy+c\] Þ \[x=c{{e}^{y}}-y-2\].


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