求dy/dx-(1/x)y=2x^2的通解

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/07/11 21:18:37

∵dy/dx-(1/x)y=2x^2
==>dy-ydx/x=2x^2dx
==>dy/x-ydx/x^2=2xdx (等式两端同除x)
==>d(y/x)=d(x^2)
==>y/x=x^2+C (C是常数)
==>y=x^3+Cx
∴原方程的通解是y=x^3+Cx.

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