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JEE Main & Advanced Mathematics Differential Equations Question Bank Variable Separable type differential equations

  • question_answer
    The solution of differential equation \[x\frac{dy}{dx}+y={{y}^{2}}\] is

    A)                 \[y=1+cxy\]          

    B)                 \[y=\log \{cxy\}\]

    C)                 \[y+1=cxy\]          

    D)                 \[y=c+xy\]

    Correct Answer: A

    Solution :

                       \[x\frac{dy}{dx}+y={{y}^{2}}\] Þ \[x\frac{dy}{dx}={{y}^{2}}-y\]                    Þ \[\frac{dy}{{{y}^{2}}-y}=\frac{dx}{x}\] Þ \[\left[ \frac{1}{y-1}-\frac{1}{y} \right]dy=\frac{dx}{x}\]                    On integrating, we get \[\log (y-1)-\log y=\log x+\log c\]                                 Þ \[\frac{y-1}{y}=xc\] Þ \[y=1+cxy\].


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