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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        The solution of\[y\text{ }dx-x\text{ }dy+3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}\text{ }dx=0\]is.

    A)  \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]                         

    B)  \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\]

    C)  \[-\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]       

    D)  None of these

    Correct Answer: A

    Solution :

                    Given differential equation can be rewritten as \[\frac{y\,dx-x\,dy}{{{y}^{2}}}+3{{x}^{2}}{{e}^{{{x}^{3}}}}dx=0\] \[\Rightarrow \]               \[d\left( \frac{x}{y} \right)+d({{e}^{{{x}^{3}}}})=0\] On integrating, we get                 \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]


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