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JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The differential equation of the family of curves \[y=A{{e}^{3x}}+B{{e}^{5x}},\]where A and B are arbitrary constants, is [MNR 1988]

    A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+8\frac{dy}{dx}+15y=0\]      

    B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+15y=0\]

    C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\] 

    D) None of these

    Correct Answer: B

    Solution :

    • \[y=A{{e}^{3x}}+B{{e}^{5x}}\]                   
    • Þ \[\frac{dy}{dx}=3A{{e}^{3x}}+5B{{e}^{5x}}\]Þ\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=9A{{e}^{3x}}+25B{{e}^{5x}}\]                   
    • Þ \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+15y=0\](By inspection)


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