Given (y=e^{m\sin^{-1}x}). Differentiate with respect to (x): [ y_1=\frac{dy}{dx}=e^{m\sin^{-1}x}\cdot \frac{m}{\sqrt{1-x^2}}=\frac{m}{\sqrt{1-x^2}},y. ] Differentiate again: [ y_2=\frac{d}{dx}\left(\frac{m}{\sqrt{1-x^2}}y\right) =\frac{m}{\sqrt{1-x^2}}y_1+\frac{mx}{(1-x^2)^{3/2}}y. ] Substitute (y_1=\frac{m}{\sqrt{1-x^2}}y): [ y_2=\frac{m^2}{1-x^2}y+\frac{mx}{(1-x^2)^{3/2}}y. ] Now compute [ (1-x^2)y_2-xy_1-m^2y. ] Using the expressions