JEE Main & Advanced Mathematics Differential Equations Question Bank Self Evaluation Test - Differential Equations

  • question_answer
    The general solution of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos \,\,nx\] is

    A) \[{{n}^{2}}y+\cos \,\,nx={{n}^{2}}(Cx+D)\]

    B) \[{{n}^{2}}y-sin\,\,nx={{n}^{2}}(-Cx+D)\]

    C) \[{{n}^{2}}y+\cos \,\,nx=\frac{Cx+D}{{{n}^{2}}}\]

    D) None of these. [Where C and D are arbitrary constants]

    Correct Answer: A

    Solution :

    [a] The differential equation is \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos nx\] Integrating we get \[\frac{dy}{dx}=\frac{\sin nx}{n}+C\]                              ? (i) Integrating again \[y=-\frac{\cos nx}{{{n}^{2}}}+Cx+D\] \[\Rightarrow {{n}^{2}}y+\cos nx={{n}^{2}}(Cx+D)\]

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