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JEE Main & Advanced Mathematics Differential Equations Question Bank Application of differnetial equations

  • question_answer
    The equation of the curve through the point (1,0) and whose slope is \[\frac{y-1}{{{x}^{2}}+x}\]is

    A)                 \[(y-1)(x+1)+2x=0\]          

    B)                 \[2x(y-1)+x+1=0\]

    C)                 \[x(y-1)(x+1)+2=0\]          

    D)                 None of these

    Correct Answer: A

    Solution :

                       Slope \[=\frac{dy}{dx}\]                    Þ \[\frac{dy}{dx}=\frac{y-1}{{{x}^{2}}+x}\]Þ\[\frac{dy}{y-1}=\frac{dx}{{{x}^{2}}+x}\]                    Þ\[\int_{{}}^{{}}{\frac{1}{y-1}}dy=\int_{{}}^{{}}{\left( \frac{1}{x}-\frac{1}{x+1} \right)\text{ }}dx+c\]Þ\[\frac{(y-1)(x+1)}{x}=k\]                    Putting \[x=1\],\[y=0\], we get \[k=-2\]                                 Hence the equation is \[(y-1)(x+1)+2x=0\].


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