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JEE Main & Advanced Mathematics Differential Equations Question Bank Exact defferential equations

  • question_answer
    The solution of the differential equation, \[y\,dx+(x+{{x}^{2}}y)dy=0\] is              [AIEEE 2004]

    A)                 \[\log y=cx\]          

    B)                 \[-\frac{1}{xy}+\log y=c\]

    C)                 \[-\frac{1}{xy}+\log y=c\]  

    D)                 \[-\frac{1}{xy}+\log y=c\]

    Correct Answer: B

    Solution :

                       \[ydx+xdy=-{{x}^{2}}ydy\] Þ \[\frac{1}{{{(xy)}^{2}}}dxy=-\frac{dy}{y}\]                    Integrating both side we get                                 \[-\frac{1}{xy}=-\log y+c\] Þ \[-\frac{1}{xy}+\log y=c\].             


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