[" thow that "y=e^(m sin^(-1)x)" is a selu "],[" of die "(1-x^(2))y_(2)-xy" ,"-m^(2)y=0" ."]

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

" 1(a) If "y=e^(a sin^(-1)x)" ,show that "(1-x^(2))y_(2)-xy_(1)-a^(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 = sin(mcos^(-1)x) then prove that (1-x^(2))y_(2)-xy_(1)+m^(2)y=0 .

If y=e^(m sin ^(-1)x) , then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0 .

If y = e^(m sin^-1 x) -1lexle1 , show that : (1- x^2)y_2 - x y_1 - m^2y = 0 .

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

Verify that y=e^(m sin^(-1)x) is a solution of the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0.

14.If y=e^(m sin^(-1)x) find the value of (y_(2))_(0)

If y=e^(m sin^(-1)x) then prove that (1-x^2) y_2 - xy_1 = m^2 y