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JEE Main & Advanced Mathematics Differential Equations Question Bank Mock Test - Differential Equations

  • question_answer
    The solution to the differential equation\[y\log y+xy'=0\], where \[y(1)=e\], is

    A) \[x(log\,y)=1\]   

    B) \[xy(log\,y)=1\]

    C) \[{{(log\,y)}^{2}}=2\] 

    D) \[\log y+\left( \frac{{{x}^{2}}}{2} \right)y=1\]

    Correct Answer: A

    Solution :

    [a] \[x\frac{dy}{dx}+y(log\,y)=0\] Or \[\int{\frac{dx}{x}+\int{\frac{dy}{y(log\,y)}=c}}\] Or \[\log x+\log (log\,y)=log\,c\] Or \[x\log y=c\] \[y(1)=e\] \[\Rightarrow c=1\] Hence, the equation of the curve is x log y=1


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