JEE Main & Advanced Mathematics Differential Equations Question Bank Self Evaluation Test - Differential Equations

  • question_answer
    The solutions of \[(x+y+1)\text{ }dy=dx\] are

    A) \[x+y+2=C{{e}^{y}}\]

    B) \[x+y+4=C\,log\,y\]

    C) \[\log (x+y+2)=Cy\]

    D) \[\log (x+y+2)=C-y\]

    Correct Answer: A

    Solution :

    [a] Putting \[x+y+1=u,\] we have \[du=dx+dy\]and the given equation reduces to \[u(du-dx)=dx\] \[\Rightarrow \frac{udu}{u+1}=dx\Rightarrow u-\log (u+1)=x\] \[\Rightarrow \log (x+y+2)=y+constant\Rightarrow x+y+2=C{{e}^{v}}\]

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