If `x=a e^t(sint+cost)` and `y=a e^t(sint-cost),` prove that `(dy)/(dx)=(x+y)/(x-y)dot`

Explanation

`x = ae^t(sint+cost), y = ae^t(sint-cost) `

`=> dx/dt = (sint+cost)ae^t +ae^t(cost-sint) = x-y`

`=>dy/dt = (sint-cost)ae^t +ae^t(cost+sint) = x+y`

`:. dy/dx = (dy/dt)/(dx/dt) = (x+y)/(x-y)`

`=>dy/dx = (x+y)/(x-y)`