1.

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

Answer» `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)`


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