`A = [{:(e^(t), e^(-t)"cos"t, e^(-t)"sin"t),(e^(t)-e^(-t), "cos"t-e^(-t)"sin"t, -e^(-t)"sin"t + e^(-t)"cos"t),(e^(t), 2e^(-t)"sin"t, -2e^(-t)"cos"t):}]"then A is"`

x = e^(-t) (a cos t + b sin t )

int e^(t)(cost-sin t)dt

int(2e^(t))/(e^(3t)-6e^(2t)+11e^(t)-6)dt

Matrix [[e^t,e^(-t)(sint-2cost),e^(-t)(-2sint-cost)],[e^t,-e^(-t)(2sint+cost),e^(-t)(sint-2cost)],[e^t,e^(-t)cost,e^(-t)sint]] is invertible. (1) only id t=pi/2 (2) only y=pi (3) t in R (4) t !in R

If x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=

If x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=

The equations x=(e^t+e^(-t))/2,y=(e^(t)-e^(-t))/2, t inR represent :