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If `y="sin"(logx),`then prove that `(x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0` |
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Answer» `y = sin(logx)` `dy/dx = cos(logx)*1/x` `=>xdy/dx = cos(logx)` Again differentiating w.r.t. `x`, `=>x(d^2y)/dx^2 + dy/dx = -sin(logx)*1/x` `=>x(d^2y)/dx^2+dy/dx = -y/x` `=>x^2(d^2y)/dx^2+xdy/dx+y = 0` |
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