A function is reprersented parametrically by the equations `x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof|(dy)/(dx)-x((dy)/(dx))^3|` is__________

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))

Solve the equation (dy)/(dx)+1/x=(e^y)/(x^2)

if x=(1+t)/t^3 ,y=3/(2t^2)+2/t satisfies f(x)*{(dy)/(dx)}^3=1+(dy)/(dx) then f(x) is:

if x=(1+t)/t^3 ,y=3/(2t^2)+2/t satisfies f(x)*{(dy)/(dx)}^3=1+(dy)/(dx) then f(x) is:

A curve parametrically given as x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2)

T h ev a l u eof(pi^2)/(1n3)int_(7/6)^(5/6)sec(pix)dxi s____

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

(dy)/(dx) + 3y = e^(-2x)

A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2) ?