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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

  • question_answer
    The general solution of the differential equation \[2x\frac{dy}{dx}-y=3\] is a family of

    A) hyperbolas      

    B) parabolas

    C) straight lines   

    D) circles

    Correct Answer: B

    Solution :

    The given differential equation is \[2x\frac{dy}{dx}-y=3\] \[\Rightarrow \]               \[2x\frac{dy}{dx}=(y+3)\] \[\Rightarrow \]               \[2\int{\frac{dy}{(y+3)}}=\int{\frac{dx}{x}}\]       (on integrating) \[\Rightarrow \]               \[2\log (y+3)=\log x+\log c\] \[\Rightarrow \]               \[{{(y+3)}^{2}}=cx\] Which represents a family of parabolas.


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