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JEE Main & Advanced Mathematics Differential Equations Question Bank Order and degree of differential equations

  • question_answer
    The degree of the differential equation \[y(x)=1+\frac{dy}{dx}+\frac{1}{1.2}{{\left( \frac{dy}{dx} \right)}^{2}}+\frac{1}{1.2.3}{{\left( \frac{dy}{dx} \right)}^{3}}+...\] is [Orissa JEE 2005]

    A)                 2             

    B)                 3

    C)                 1             

    D)                 None of these

    Correct Answer: C

    Solution :

                       \[y=1+t+\frac{{{t}^{2}}}{2!}+\frac{{{t}^{3}}}{3!}+...+\infty \] where \[t=\frac{dy}{dx}\]                                 Þ \[y={{e}^{t}}\], \ \[t=\log y\] Þ \[\frac{dy}{dx}=\log y\]. Hence degree is 1.


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