if `y=x^2/2+1/2 xsqrt(x^2+1)+lnsqrt(x+sqrt(x^2+1))` prove that `2y=xy'+lny'`

If y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)_esqrt(x+sqrt(x^2+1)) , prove that 2y=x y^(prime)+(log)_e y^(prime),w h e r ey ' denotes the derivative w.r.t xdot

If quad (x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1))y=(x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)) prove that 2y=xy'+log_(e)y', where y' denotes the derivative w.r.x.

If y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+lnsqrt(x+sqrt(x^(2)+1)) then the value of xy'+logy' is

If y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+lnsqrt(x+sqrt(x^(2)+1)) then the value of xy'+logy' is

If y = log (x + sqrt(x^2+1))/(sqrt(x^2+1)) , prove that (x^2 +1) dy/dx + xy = 1

"If "y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)), then

"If "y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)), then

If y sqrt(x^(2)+1)= log (sqrt(x^(2)+1)-x) , prove that (x^(2)+1)(dy)/(dx) +xy+1=0 .

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_1-xy=1

If y = (sqrt(x+1) - sqrt(x-1)) , then prove that (x^2-1) y_2 +xy_1 = 1/4 y