[y=x^(2)cos x],[" Prove that "x^(2)y_(2)-4xy_(1)+(x^(2)+6)y=0]

IF y=x^2 cosx, prove that , x^2y_2-4xy_1+(x^2+6)y=0 .

y=x^2 cosx then prove that x^2y_2-4xy_1+(x^2+6)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=x^(2)+x^(-2)," then "x^(2)y_(2)+4xy_(1)+2y=

If y=(cos^(-1)x)^(2) , then prove that : (1-x^(2))y_(2)-xy_(1)-2=0 .

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

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

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

(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=a cos (logx)+b sin (logx) , prove that x^(2)y_(2)+xy_(1)+y=0 .