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

  • question_answer
    Solution of the differential equation \[\frac{dy}{dx}+\frac{y}{x}=\sin x\] is [Kerala (Engg.) 2005]

    A)                 \[x(y+\cos x)=\sin x+c\]     

    B)                 \[x(y-\cos x)=\sin x+c\]

    C)                 \[x(y\cdot \cos x)=\sin x+c\]

    D)                 \[x(y-\cos x)=\cos x+c\]

    E)                 \[x(y+\cos x)=\cos x+c\]

    Correct Answer: A

    Solution :

                       \[\frac{dy}{dx}+\frac{y}{x}=\sin x\]; I.F.\[={{e}^{\int{\frac{1}{x}dx}}}={{e}^{\log x}}=x\] \ \[yx=\int{x\sin xdx}\] Þ \[yx=\int{x\sin xdx}\] Þ \[xy=-x\cos x+\sin x+c\] Þ \[x(y+\cos x)=\sin x+c\].


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