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