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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 \[(1+\cos x)dy=(1-\cos x)dx\]is

    A)                 \[y=2\tan \frac{x}{2}-x+c\]

    B)                 \[y=2\tan x+x+c\]

    C)                 \[y=2\tan \frac{x}{2}+x+c\]              

    D)                 \[y=x-2\tan \frac{x}{2}+c\]

    Correct Answer: A

    Solution :

                       Here \[\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}={{\tan }^{2}}\frac{x}{2}\] Þ \[dy=\left( {{\sec }^{2}}\frac{x}{2}-1 \right)\,dx\]                    Now on integrating both the sides, we get                                 \[y=2\tan \frac{x}{2}-x+c\].


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