Question

1) y'=y
2) x+xy-y'(y+xy)=0
3) yy'+x=0
Срочно помогите решить!!!
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Answer 1

1)dy/y=dx ln|y|=x+c |y|=e^(x+c)
2)x(1+y)-ydy/dx(1+x)=0
x(1+y)=y(1+x)dy/dx
xdx/(1+x)=ydy/(1+y)
(1-1/(1+x))dx=(1-1/(1+y))dy
x-ln|x+1|=y-ln|y+1|
y-x=ln|(y+1)/(x+1)|
y=x+ln|(y+1)/(x+1)|
3)ydy/dx=-x
ydy=-xdx
y^2/2=-x^2/2+c
y^2=-x^2+C1
y=(C1-x^2)^1/2