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∵(x-2)*dy/dx=y+2*(x-2)³
==>(x-2)dy=[y+2*(x-2)³]dx
==>(x-2)dy-ydx=2*(x-2)³dx
==>[(x-2)dy-ydx]/(x-2)²=2*(x-2)dx
==>d[y/(x-2)]=d[(x-2)²]
==>y/(x-2)=(x-2)²+C
(C是积分常数)
==>y=(x-2)³+C(x-2)
∴原方程的通解是y=(x-2)³+C(x-2)
(C是积分常数).
==>(x-2)dy=[y+2*(x-2)³]dx
==>(x-2)dy-ydx=2*(x-2)³dx
==>[(x-2)dy-ydx]/(x-2)²=2*(x-2)dx
==>d[y/(x-2)]=d[(x-2)²]
==>y/(x-2)=(x-2)²+C
(C是积分常数)
==>y=(x-2)³+C(x-2)
∴原方程的通解是y=(x-2)³+C(x-2)
(C是积分常数).
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