作业帮..微分方程...
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/13 12:00:59
..微分方程...
∵y'=sin²(x-y+1) ==>dy/dx=sin²(x-y+1)
==>1-dy/dx=1-sin²(x-y+1)
==>(dx-dy)/dx=cos²(x-y+1)
==>d(x-y)/dx=cos²(x-y+1)
==>d(x-y+1)/dx=cos²(x-y+1)
==>d(x-y+1)/cos²(x-y+1)=dx
==>sec²(x-y+1)d(x-y+1)=dx
==>tan(x-y+1)=x+C (C是积分常数)
∴原方程的通解是tan(x-y+1)=x+C (C是积分常数).
==>1-dy/dx=1-sin²(x-y+1)
==>(dx-dy)/dx=cos²(x-y+1)
==>d(x-y)/dx=cos²(x-y+1)
==>d(x-y+1)/dx=cos²(x-y+1)
==>d(x-y+1)/cos²(x-y+1)=dx
==>sec²(x-y+1)d(x-y+1)=dx
==>tan(x-y+1)=x+C (C是积分常数)
∴原方程的通解是tan(x-y+1)=x+C (C是积分常数).