If y=log (1+ sin x), prove that `y_(4)+y_(3)y_(1)+y_(2)^(2)=0`.

If y=3cos(log x)+4sin(log x), prove that x^(2)y_(2)+xy_(1)+y=0

If y=3 cos(log x)+4 sin(log x), show that x^(2)y_(2)+xy_(1)+y=0

If y = x log (x/(a+bx)) , prove that x^3 y _2 = (xy_1 - y)^2

(a) If y=cos(msin^(-1)x) prove that (1-x^(2))y_(3)-3xy_(2)+(m^(2)-1)y_(1)=0 (b) Find y'' if x^(4)+y^(4)=16 .

If y=(sin^(-1)x)^(2), prove that (1-x^(2))y_(2)-xy_(1)-2=0

If y=3cos(log x)+4sin(log x), show that x^(2)y_(2)+xy_(1)+y=0

If cos^(-1)((y)/(b))=log((x)/(n))^(n) , prove that, x^(2)y_(2)+xy_(1)+n^(2)y=0 .

If y = sin^-1x , prove that (1-x^2)y_2 - x y_1= 0

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .