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討論串[微積] 微分方程
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[2x-ysin(xy)]dx + [3y^2 - xsin(xy)]dy =0. (2xdx + 3y^2 dy) -[sin(xy)][ydx +xdy] =0. d(x^2) + d(y^3) -sin(xy)d(xy) =0. 兩端積分得. x^2 + y^3 +cos(xy) = Cons
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不行. 第一式子是exact. ∫{2x - ysin(xy)}@x = x^2 + cos(xy) + h(y). ∫ {3y^2 - xsin(xy)}@y = y^3 + cos(xy) + r(x). 所以你只寫對一半. x^2 + y^3 + 2cos(xy) + h(y) + r(x)
(還有103個字)
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看解答看不懂. 2x - ysin(xy) + {3y^2-xsin(xy)}y' = 0 <= 解微分方程. 解答： {2x-ysin(xy)} dx + {3y^2 - xsin(xy)}dy = 0. d{x^2 + ysin(xy) +y^3} = 0. x^2 + cos(xy) + y^
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