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" 8.If "y=x^(x)," prove that "(d^(2)y)/(...

" 8.If "y=x^(x)," prove that "(d^(2)y)/(dx^(2))-(1)/(y)((dy)/(dx))^(2)-(y)/(x)=0

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If y=x^(x) , then prove that (d^(2)y)/(dx^(2))-(1)/(y)((dy)/(dx))^(2)-(y)/(x)=0

if y=x^(x), then prove (d^(2)y)/(dx^(2))-(1)/(y)((dy)/(dx))^(2)-(y)/(x)=0

If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

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If y=e^(x)sinx, prove that (D^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 .

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If y=x^(3)log((1)/(x)) , prove that (d^(2)y)/(dx^(2))-(2)/(x)(dy)/(dx)+3x=0 .

If y=log(1+cos x), prove that (d^(3)y)/(dx^(3))+(d^(2)y)/(dx^(2))(dy)/(dx)=0