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Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    If the solution of the differential equation\[\frac{dy}{dx}=\frac{ax+3}{2y+f}\]represents a circle, then the value of\[a\]is

    A)  2                                            

    B)  -2

    C)  3                                            

    D)  -4

    Correct Answer: B

    Solution :

    We have,\[\frac{dy}{dx}=\frac{ax+3}{2y+f}\] \[\Rightarrow \]               \[(ax+3)dx=(2y+f)dy\] On integrating, we obtain                 \[a\frac{{{x}^{2}}}{2}+3y={{y}^{2}}+fy+c\] \[\Rightarrow \]               \[-\frac{a}{2}{{x}^{2}}+{{y}^{2}}-3x+fy+c=0\] This will represent a circle, if                 \[-\frac{a}{2}=1\]                 (\[\because \]coefficient of\[{{x}^{2}}=\]coefficient of\[{{y}^{2}}\]) \[\Rightarrow \]               \[a=-2\]


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