1) xy'-y=-x^3
2) xy'+y(ln(y/x)-1)=0
1) y'-y/x=-x^2, y'=y/x+x^2, , , ?
2) y/x=t, y=tx, y'=t'x+t, x=y/t/?
(t'x+t)y/t=-tx(lnt-1). ! - ?
2) xy'+tx(lnt-1)=0
y'+t(lnt-1)=0
y'=-t(lnt-1)
y =- t^2/2 lnt ,
y=-y^2/2x^2 - lny/x
xt'x+t+tx(lnt-1)=0
x^2t'+t+xt(lnt-1)=0
(t'x+t)+tx(lnt-1)=0;
t'*x^2+tx+tx*ln(t)-tx=0;
t'*x+t*ln(t)=0.
y'+a(x)*y=b(x), y=u*v,:
u'v+uv'+a(x)*uv=b(x);
u'v+u*(v'+a(x)*v)=b(x);
v v'+v*a(x)=0, , u .
u'v+uv'-1/x*uv=-x^2
u'v+u(v'-1/x*v)=-x^2
v'-1/x*v=0
v'=1/x*v
v'/v=1/x
dv/v=dx/x
lnv=lnx
lnv=lnx
v=x
u'*x=-x^2
u'=-x
u=-x^2/2
y=-x^2/2*x
y=-x^3/2