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JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The solution of \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos x-\sin x\]is

    A) \[y=-\cos x+\sin x+{{c}_{1}}x+{{c}_{2}}\]                  

    B) \[y=-\cos x-\sin x+{{c}_{1}}x+{{c}_{2}}\]                          

    C) \[y=\cos x-\sin x+{{c}_{1}}{{x}^{2}}+{{c}_{2}}x\]       

    D) \[y=\cos x+\sin x+{{c}_{1}}{{x}^{2}}+{{c}_{2}}x\]

    Correct Answer: A

    Solution :

    • \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos x-\sin x\]. On integrating both sides, we get        
    • \[\frac{dy}{dx}=\sin x+\cos x+{{c}_{1}}\]                   
    • Again \[y=-\cos x+\sin x+{{c}_{1}}x+{{c}_{2}}\].


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