1
xy''=y'-x(y')^2
xy''/(y')^2-y'/(y')^2=-x
d(x/y')/dx=(xy''-y')/(y')^2
d(x/y')=-xdx
x/y'=-x^2/2
1/y'=-x/2
dx/dy=-x/2
dx/x=-dy/2
lnx=-y/2+C
y=-ln(x^2)+C'
2
y''+2y'=0
y''/y'=-2
(lny')'=2
d(lny')/dx=2
lny'=2x+C
y'=Ce^(2x)
dy/dx=Ce^(2x)
dy=Ce^(2x)dx
y=C'e^(2x)