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JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    Let \[y=f(x)\] be a function satisfying the differential equation \[\frac{xdy}{dx}=2y=4{{x}^{2}}\] and \[f(1)=1\], then \[f(x)\] Mas equal to

    A) \[-3\]                                    

    B) 0

    C) 3                                             

    D) 9

    Correct Answer: D

    Solution :

    \[\frac{dy}{dx}+\left( \frac{2}{x} \right)y=4x\] (Linear differential equation) I.F. \[={{e}^{2\int{\frac{dx}{x}}}}={{x}^{2}}\] So, \[y.{{(x)}^{2}}=\int{{}}(4x){{x}^{2}}dx+c\Rightarrow y{{(x)}^{2}}={{x}^{4}}+c\] As, \[y(1)=1\Rightarrow 1=1+c=0\] \[f(x)={{x}^{2}}\Rightarrow f(-3)=9\]


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