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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 \[\frac{dy}{dx}={{x}^{2}}+\sin 3x\] is [DSSE 1981]

    A)                 \[y=\frac{{{x}^{3}}}{3}+\frac{\cos 3x}{3}+c\]          

    B)                 \[y=\frac{{{x}^{3}}}{3}-\frac{\cos 3x}{3}+c\]

    C)                 \[y=\frac{{{x}^{3}}}{3}+\sin 3x+c\]            

    D)                 None of these

    Correct Answer: B

    Solution :

                    \[\frac{dy}{dx}={{x}^{2}}+\sin 3x\]. On integrating, \[y=\frac{{{x}^{3}}}{3}-\frac{\cos 3x}{3}+c\].


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