Question

高等数学经管类 一阶线性微分方程

Answer 1

∵(x-2)dy/dx=y+2(x-2)^3

==>(x-2)dy-ydx=2(x-2)^3dx

==>dy/(x-2)-ydx/(x-2)^2=2(x-2)dx (等式两端同除(x-2)^2)

==>dy/(x-2)+yd(1/(x-2))=2(x-2)d(x-2)

==>d(y/(x-2))=d((x-2)^2)

==>y/(x-2)=(x-2)^2+C (C是常数)

==>y=(x-2)^3+C(x-2)

∴原方程的通解是y=(x-2)^3+C(x-2).