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JEE Main & Advanced Sample Paper JEE Main Sample Paper-31

  • question_answer
    If \[xdy=y(dx+ydy),y(1)=1\] and \[y(x)>0\], then \[y(-3)\] is equal to

    A) 1                                             

    B) 2

    C) 3             

    D) 4

    Correct Answer: C

    Solution :

    Given, \[\frac{xdy-ydx}{{{y}^{2}}}=dy\Rightarrow d\left( \frac{x}{y} \right)=-dy\Rightarrow \frac{x}{y}=-y+C\]                 As, \[y(1)=1\Rightarrow C=2\Rightarrow \frac{x}{y}+y=2\]                 Put\[x=-3,\] we get \[-3+{{y}^{2}}=2y\Rightarrow (y+1)(y-3)=0\]       As \[y>0\] As, \[y(x=-3)=3\]


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