微分方程(2x-y)dx+(2y-x)dy=0的通解

(2x - y)dx + (2y - x)dy = 0∂(2x - y)/∂y = - 1 = ∂(2y - x)/∂x,这是全微分方程∫ (2x - y) dx = x² - xy + h(y)∂[x² - xy + h(y)]/∂y = - x + h'(y)- x + h'(y) = 2y - x=> h'(y) = 2y=> h(y) = y²所以通解为x² - xy + y² = C