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" 亲了.If "y=e^(nx)," prove that "y(n)=n^(...

" 亲了.If "y=e^(nx)," prove that "y_(n)=n^(n)e^(nx)

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If x^(m)y^(n)=1, prove that (dy)/(dx)=-(my)/(nx)

If y=Ae^(mx)+Be^(nx) , prove that (d^(2)y)/(dx^(2)) -(m+n) (dy)/(dx) + mny=0 .

If y=ae^(nx)+be^(-nx) , then prove that y''=n^(2)y .

If x + y = 1 , prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r) = nx .

If x + y = 1 , prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r) = nx .

if y=Ae^(mx)+Be^(nx) then prove that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+mny=0

If y= Ae^(mx)+Be^(nx) prove that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+ (mn)y=0