Re: [理工] [工數]-一階ODE
第二題
這題不難工程浩大＝ ＝
令x＝u+1 du＝dx y＝v dv＝dy
帶入
（u-v）du+（4v+u）dv＝0
令 z＝u/v du＝zdv+vdz
帶入
（z-1）（zdv+vdz）+（4+z）dv＝0
（z-1）/z^+4 dz=-1/v dv
積分
ln(z^2+4)/2-tan^-1(z/x)/x=-lnv+lnc
左右同乘2還原
ln[(x-1)^2+4y^2]-ln(y^2)-tan^-1(x-1/2y)＝-2lny+lnc
ln[(x-1)^2+4y^2]-tan^-1(x-1/2y)＝lnc
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by新宿事件
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