If `y=log_e(x/(a+b x))^x` , then `x^3y_2` is (a) `(x y_1-y)^2` (b) `(1+y)^2` (c) `((y-x y_1)/(y_1))^2` (d) none of these

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If y=(log)_e(x/a)^x ,then x^3y_2= (a) (xy_1-y)^2 (b) ((y-x y_1)/(y_1))^2 (c) none of these

If y=(log)_(e)((x)/(a))^(x), thenx ^(3)y_(2)=b)(xy_(1)-y)^(2).(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these

If y=sin(m\ sin^(-1)x) , then (1-x^2)y_2-x y_1 is equal to m^2y (b) m y (c) -m^2y (d) none of these

If y=e^(tan x), then (cos^(2)x)y_(2)=(1-sin2x)y_(1)(b)-(1+sin2x)y_(1)(c)(1+sin2x)y_(1)(d) none of these

If y=(a x+b)/(x^2+c), then (2x y_1+y) y_3=

The differential equation of all circle in the first quadrant touch the coordinate is (a) (x-y)^(2)(1+y')^(2)=(x+yy')^(2) (b) (x-y)^(2)(1+y')^(2)=(x+y')^(2) ( c ) (x-y)^(2)(1+y')=(x+yy')^(2) (d) None of these

The differential equation of all circle in the first quadrant touch the coordinate is (a) (x-y)^(2)(1+y')^(2)=(x+yy')^(2) (b) (x-y)^(2)(1+y')^(2)=(x+y')^(2) ( c ) (x-y)^(2)(1+y')=(x+yy')^(2) (d) None of these

y=log_e((1+x^2)/(1-x^2)) then find 225(y''-y') at x=1/2