[dx^(2)],[quad " (ii) "x=at^(2),y=2at]

Find (dy)/(dx) if, (i) x=at^2, y=2at (ii) x=2at^2, y=at^4 (iii) x=e^(3t),y=e^(4t+5)

Find frac(d^2y)(dx^2) : (ii) x = a cos theta, y = b sin theta

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

Find (d^2y)/(dx^2) , when (i) x^2/a^2+y^2/b^2=1 (ii) y= sin (x+y).

(i). If y=x^(3)-1 , find (dy)/(dx) . (ii). If y=2x^(2)+4 , find (dy)/(dx)

Solve the differential equation: (i) (1+y^(2))+(x-e^( tan ^(-1)y))(dy)/(dx)=0 (ii) x(dy)/(dx)+cos^(2)y=tan y(dy)/(dx)

Differentiate with respect to X (i) y=xlnx " " (ii) y=x^(2)e^(x) " " (iii) y=(sin x)/(x) " " (iv) y=(3x^(2)+2sqrt(x))/(x)

(i) If y^(1//m) + y^(-1//m) = 2x , then prove that (x^(2)-1) (d^(2)y)/(dx^(2)) + x (dy)/(dx) - m^(2)y =0 (ii) If y = ln (x + sqrt(1+x^(2))) , then prove that (1+x^(2)) (d^(2)y)/(dx^(2)) + x (dy)/(dx)=0