Question

微分方程的问题

4xy+2x+(2x^2+3y^2)y'=0
4xy+2yx^2+(2x^2+3y^2)y'=0
2cos(x+y)-2xsin(x+y)-2xsin(x+y)y'=0
1/x+y+(3y^2+x)y'=0
y+e^x+xy'=0
3y^4-1+12xy^3y'=0
麻烦大家帮忙做下这几道微分方程，先谢谢了

Answer 1

Answer 2

1
4xy+2x+(2x^2+3y^2)y'=0
yd(2x^2)+2x^2dy+dx^2+dy^3=0
2x^y+x^2+y^3=C
2
4xy+2yx^2+(2x^2+3y^2)y'=0
4xydx+2yx^2dx+2x^2dy+3y^2dy=0

3
2cos(x+y)-2xsin(x+y)-2xsin(x+y)y'=0
dx/x=-dcos(x+y)/cos(x+y)
lnx=C-lncos(x+y)
4
1/x+y+(3y^2+x)y'=0
dx/x+d(xy+3y^2)=0
lnx+xy+y^3=C
5
y+e^x+xy'=0
d(xy+e^x)=0
xy+e^x=C
6
3y^4-1+12xy^3y'=0
3y^4dx-dx+xd(3y^4)=0
3xy^4-x=C