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

  • question_answer
    \[y=2\,cos\text{ }x+3\,sin\text{ }x\] satisfies which of the following differential equations?
    1. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
    2. \[{{\left( \frac{dy}{dx} \right)}^{2}}+\frac{dy}{dx}=0\]
    Select the correct answer using the code given below.

    A) 1 only

    B) 2 only

    C) Both 1 and 2

    D) Neither 1 nor 2

    Correct Answer: A

    Solution :

    [a] \[y=2\cos x+3\sin x\] \[\frac{dy}{dx}=-2\sin x+3\cos x;\frac{{{d}^{2}}y}{dx}=-2\cos x-3\sin x\] \[=-(2cosx+3sinx)=-y;\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]

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