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Solve `(dy)/(dx) = sec (x+y)` |
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Answer» Setting x+y-t, we have no differentiation w.r.t. x `1+(dy)/(dx) = (dt)/(dx)` Our equation not reads `(dt)/(dx) - 1 = sec t` `rArr (dt)/(dx) = 1+ sec t` `rArr (dt)/(1+ sec t) = dx` `rArr (cos t dt)/(1+cos t) = dx` `rArr ((1+ cos t)-1)/(1+ cos t) dt = dx` `rArr dt - (dt)/(1+ cos t) = dx` `rArr dt - (dt)/(2 cos^(2).(t)/(2)) = dx` `rArr dt-(1)/(2)sec^(2).(t)/(2) dt = dx` Integrating, we get, `t- tan.(t)/(2) = x + k` `rArr x+y - tan.(x+y)/(2) =x+k` `:. y - tan.(x+y)/(2) = k`, k being the constant of integration. |
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