求一曲线的方程,这曲线通过原点,并且它在点（x,y）处的切线斜率等于2x+y

根据题意dy/dx = 2x + y 设u = 2x + y,y = u - 2x,dy/dx = du/dx - 2 即du/dx - 2 = u 分离变量 ∫du/(u + 2) = ∫dx ln(u + 2) = x + C ln(2x + y + 2) = x + C 2x + y + 2 = Ce^x y = Ce^x - 2x - 2 y(0) = C - 2 ...