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JEE Main & Advanced Mathematics Differential Equations Question Bank Linear defferential equations

  • question_answer
    Solution of the differential equation \[\frac{dy}{dx}+y{{\sec }^{2}}x=\tan x{{\sec }^{2}}x\] is         [DCE 2001, 05]

    A)                 \[y=\tan x-1+c{{e}^{-\tan x}}\]

    B)                 \[{{y}^{2}}=\tan x-1+c{{e}^{\tan x}}\]

    C)                 \[y{{e}^{\tan x}}=\tan x-1+c\]        

    D)                 \[y{{e}^{-\tan x}}=\tan x-1+c\]

    Correct Answer: A

    Solution :

                       I.F. = \[{{e}^{\int{{{\sec }^{2}}x\,dx}}}={{e}^{\tan x}}\]         \ Solution is \[y{{e}^{\tan x}}=c+\int{\tan x{{e}^{\tan x}}{{\sec }^{2}}x\,dx}\]                 Þ \[y=c{{e}^{-\tan x}}+\tan x-1\].


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