求dy/dx=2x+y的通解.

求dy/dx=2x+y的通解.

我来介绍个方法吧
令2x+y=u
两边对x求导,得
2+dy/dx=du/dx
所以
du/dx-2=u
du/dx=u+2
1/(u+2)du=dx
∫1/(u+2)du=∫dx
ln|u+2|=x+ln|c|
u+2=ce^x
2x+y+2=ce^x
y=ce^x-2x-2