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JCECE Engineering JCECE Engineering Solved Paper-2010

  • question_answer
    If \[\sin x\] is an integrating factor of the differential equation\[\frac{dy}{dx}+Py=Q\], then \[P\] can be

    A) \[\log \sin x\]                    

    B) \[\cot x\]

    C) \[\sin x\]                                             

    D) \[\log \cos x\]

    Correct Answer: B

    Solution :

    We have the differential equation                 \[\frac{dy}{dx}+Py=Q\] Integrating factor of this differential equation                           \[=\sin x\] \[\Rightarrow \]               \[{{e}^{\int{Pdx}}}=\sin x\] \[\Rightarrow \]       \[\int{Pdx}=\log \sin x\] \[\Rightarrow \]                   \[P=\frac{d}{dx}(\log \sin x)\] \[\Rightarrow \]                  \[P=\frac{1}{\sin x}\cdot \cos x\] \[\Rightarrow \]                  \[P=\cot x\]


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