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求dy/dx=(x+y)^2的通解
人气:357 ℃ 时间:2020-05-04 17:01:32
解答
dy/dx = (x + y)²令t = x + y,dt/dx = 1 + dy/dxdt/dx - 1 = t²dt/dx = (1 + t²)dt/(1 + t²) = dxarctan(t) = x + C₁x + y = tan(x + C₁)y = tan(x + C₁) - x
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