[" (e) If "y=a cos(log x)+b sin(log x)," then "],[" show that "],[qquad x^(2)(d^(2)y)/(dx^(2))=x(dy)/(dx)+y=0]

If y=3cos(log x)+4sin(log x), then show that x^(2)*(d^(2)y)/(dx^(2))+(dy)/(dx)+y=0

If y=x^(n)[a cos(log x)+b sin(log x)] , show that, x^(2)(d^(2)y)/(dx^(2))+(1-2n)x(dy)/(dx)+(n^(2)+1)y=0

If y= a cos (log x)+b sin (log x) , show that x^(2) (d^(2)y)/(dx^2)+x(dy)/(dx)+y=0 .

If y = a cos(logx) + b sin(log x) , show that, x^2(d^2y)/(dx^2)+x(dy)/(dx) + y = 0

If y=sin(log x), prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0

If y=sin(log x), prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0

If y=x^(n){a cos(log x)+b sin(log x)}, prove that x^(2)(d^(2)y)/(dx^(2))+(1-2n)(dy)/(dx)+(1+n^(2))y=0

Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0