If `y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y_2+x y_1` is (where `y_r` represents the `r t h` derivative of `y` w.r.t. `xdot` (a)`m^2y` (b) `m y^2` (c) `m^2y^2` (d) none of these

If y = sin (m sin^(-1) x), prove that (1 - x^2)y_2 -xy_1 + m^2 y = 0

If y=(x^2)/2+1/2xsqrt(x^2+1)+(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

A differential equation associated to the primitive y=a+b e^(5x)+c e^(-7x) is (where y_n is n t h derivative w.r.t. x) (a) y_3+2y_2-y_1=0( b )4y_3+5y_2-20y_1=0 (c)y_3+2y_2-35y_1=0 (d) none of these

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

Differentiate the following w.r.t. x; (x^2)/(a^2) + (y^2)/(b^2) =1

If y=sinp xa n dy_n is the n t h derivative of y , then |[y, y_1,y_2],[y_3,y_4,y_5],[y_6,y_7,y_8]|i s (a)1 (b) 0 (c) -1 (d) none of these

If y=((a x+b))/((x^2+c)) , then show that (2x y '+y)y'''=3y''(x y''+y'), where a , b , c are constants and dashes denote differentiation w.r.t. xdot

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these