JEE Main & Advanced Mathematics Differential Equations Question Bank Self Evaluation Test - Differential Equations

  • question_answer
    The solution of \[\frac{dy}{dx}=\left| x \right|\] is:

    A) \[y=\frac{x\left| x \right|}{2}+c\]

    B) \[y=\frac{\left| x \right|}{2}+c\]

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

    D) \[y=\frac{{{x}^{3}}}{2}+c\] Where c is an arbitrary constant

    Correct Answer: A

    Solution :

    [a] \[\frac{dy}{dx}=\left| x \right|\] \[\frac{dy}{dx}=x\] for \[x\ge 0;\] \[\frac{dy}{dx}=-x\] for \[x<0;\] \[\int{dy=\int{xdx}}\] \[y=\frac{{{x}^{2}}}{2}+{{C}_{1}}\]            ?. (i) \[\int{dy=-1xdx}\] \[y=-\frac{{{x}^{2}}}{2}+{{C}_{1}}\]                       ?. (ii) From (i) and (ii) \[y=\frac{x\left| x \right|}{2}+C\]

You need to login to perform this action.
You will be redirected in 3 sec spinner