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JEE Main & Advanced Mathematics Differential Equations Question Bank Variable Separable type differential equations

  • question_answer
    The solution of \[\frac{dy}{dx}={{e}^{x}}(\sin x+\cos x)\]is

    A)                 \[y={{e}^{x}}(\sin x-\cos x)+c\]     

    B)                 \[y={{e}^{x}}(\cos x-\sin x)+c\]

    C)                 \[y={{e}^{x}}\sin x+c\]   

    D)                 \[y={{e}^{x}}\cos x+c\]

    Correct Answer: C

    Solution :

                       Given equation \[\frac{dy}{dx}={{e}^{x}}(\sin x+\cos x)\]                    Þ \[dy={{e}^{x}}(\sin x+\cos x)dx\]                                 On integrating, we get \[y={{e}^{x}}\sin x+c\].


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