Question

()高等数学题目是求全微分方程的通解(x²-2xy-y²)dx-(x+y)²dy=0 答案是a²x-x²y

()高等数学题目是求全微分方程的通解(x²-2xy-y²)dx-(x+y)²dy=0
答案是a²x-x²y-xy²-1／3·y³
我不懂a是什么，我求出来a²x这一项是1/3·x³

Answer 1

(x²-2xy-y²)dx-(x²+2xy+y²)dy=0
x²dx-2xydx-y²dx-x²dy-2xydy-y²dy=0
x²dx-yd(x²)-y²dx-x²dy-xd(y²)-y²dy=0
x²dx-[yd(x²)+x²dy]-[y²dx+xd(y²)]-y²dy=0
d(x³/3)-d(x²y)-d(xy²)-y³/3=0
积分得
x³/3-x²y-xy²-y³/3=C

Answer 2

答案错了，就是1/3。

追答

顶多通解加个常数c，系数没有这么变得