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

  • question_answer
    The solution of the differential equation \[(1-{{x}^{2}})(1-y)dx=xy(1+y)dy\] is

    A)                 \[\log [x\,{{(1-y)}^{2}}]=\frac{{{x}^{2}}}{2}+\frac{{{y}^{2}}}{2}-2y+c\]

    B)                 \[\log [x{{(1-y)}^{2}}]=\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{2}+2y+c\]

    C)                 \[\log [x{{(1+y)}^{2}}]=\frac{{{x}^{2}}}{2}+\frac{{{y}^{2}}}{2}+2y+c\]

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

    Correct Answer: D

    Solution :

                       \[(1-{{x}^{2}})(1-y)dx=xy(1+y)dy\]                                 Þ \[\int_{{}}^{{}}{\frac{y(1+y)}{(1-y)}dy}=\int_{{}}^{{}}{\frac{(1-{{x}^{2}})}{x}dx}\]; Now integrate it.


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