求微分方程dy/dx+3y=8,在满足x=0,y=2时的特解.
<p>问题：求微分方程dy/dx+3y=8,在满足x=0,y=2时的特解.<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">陈诗桓的回答：<div class="content-b">网友采纳 dy/dx+3y=8,分离变量得dy/(3y-8)=-dx,ln|y-8/3|/3=-x+c,把x=0,y=2代入得c=(1/3)ln(2/3),∴ln(8/3-y)=-3x+ln(2/3),ln(4-3y/2)=-3x,4-3y/2=e^(-3x),4-e^(-3x)=3y/2,∴y=8/3-(2/3)e^(-3x).
页:
[1]