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If nth derivative of xy3 + x2y2 + x3y0 = 0 then order of its nth differential equation is,

If nth derivative of xy3 + x2y2 + x3y0 = 0 then order of its nth differential equation is, Correct Answer n+3

1. If we differentiate this equation n times then terms comes in nth order differential equation is yn+3, yn+2, yn+1, yn, yn-1, yn-2, yn-3. Hence order of differential equation becomes n+3. 2. By Leibniz rule differentiating it n times, we get Xyn+3 + nyn+2 + x2yn+2 + 2nxyn+1 + 2n(n-1)yn + x3yn + 3nx2yn-1 + 6n(n-1)xyn-2 + 6n(n-1)(n-2)yn-3 = 0 Hence order of differential equation becomes n+3.

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