[" 13.यदि "y={x+sqrt(x^(2)+1)}^(m)" हो,त...

[" 13.यदि "y={x+sqrt(x^(2)+1)}^(m)" हो,तो सिद्ध कीजिए कि- "],[qquad (x^(2)+1)y_(2)+xy_(1)-m^(2)y=0]

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If y= (x + sqrt(x^(2) + 1))^(m) then prove that, (x^(2)+1) y_(2) + xy_(1)= m^(2)y

If y={x +sqrt(x^(2)+1)}^(m) , then show that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-m^(2)y=0.

If y={x+sqrt(x^(2)+1)}^(m), show that (x^(2)+1)y_(2)+xy_(1)-m^(2)y=0

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

If y^(1//m)+y^(-1//m)=2x , then prove that (x^(2)-1)y_(2)+xy_(1)=m^(2)y^(2)

If y=cos(m sin^(-1)x), show that (1-x^(2))y_(2)-xy_(1)+m^(2)y=0

If y =e ^( m Cos ^(-1)x) then show that (1- x^(2)) y _(2) - xy_(1) -m^(2) y =0.

If y=e^(msin^(-1)x),-1lexle1 , show that : (1-x^(2))y_(2)-xy_(1)-m^(2)y=0 .

If x=sin((1)/(a)log y), show that (1-x^(2))y_(2)-xy_(1)-a^(2)y=0