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

  • question_answer
    The solution of the differential equation \[\frac{dy}{dx}=(a{{e}^{bx}}+c\cos mx)\] is

    A)                 \[y=\frac{a{{e}^{x}}}{b}+\frac{c}{m}\sin mx+k\]     

    B)                 \[y=a{{e}^{x}}+c\sin mx+k\]

    C)                 \[y=\frac{a{{e}^{bx}}}{b}+\frac{c}{m}\sin mx+k\]  

    D)                 None of these

    Correct Answer: C

    Solution :

                       \[\frac{dy}{dx}=(a{{e}^{bx}}+c\cos mx)\] Þ \[dy=(a{{e}^{bx}}+c\cos mx)dx\]                                 On integrating, \[y=\frac{a{{e}^{bx}}}{b}+\frac{c\sin (mx)}{m}+k\].


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