求解方程dy/dx-2y/x+1=(x+1)^5/2的通解

dy/dx-2y/(x+1)=(x+1)^(5/2)
x+1=u dx=du
dy/du-2y/u=u^(5/2)
y/u=s dy=uds+sdu
uds/du+s-2s=u^(5/2)
uds/du-s=u^(5/2)
uds-sdu=u^(5/2)du
(uds-sdu)/u^2=u^(1/2)du
d(s/u)=(2/3)du^(3/2)+C
s/u=(2/3)u^(3/2)+C
y/u^2=(2/3)u^(3/2)+C
y=(2/3)u^(7/2)+Cu^2
通解y=(2/3)(x+1)^(7/2)+C(x+1)^2