【求微分方程的通解.y#39;#39;-6y#39;+9y=6e^3x求微分方程的通解y#39;#39;-6y#39;+9y=6e^3x】
<p>问题：【求微分方程的通解.y#39;#39;-6y#39;+9y=6e^3x求微分方程的通解y#39;#39;-6y#39;+9y=6e^3x】<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">包克亮的回答：<div class="content-b">网友采纳 特征方程为t^2-6t+9=0,t=3 所以通解为y1=(C1x+C2)e^(3x) 设特解y2=Ax^2e^(3x) 则y2'=(3Ax^2+2Ax)e^(3x) y2''=(9Ax^2+6Ax+6Ax+2A)e^(3x)=(9Ax^2+12Ax+2A)e^(3x) 所以9Ax^2+12Ax+2A-18Ax^2-12Ax+9Ax^2=6 A=3 所以y=y1+y2=(3x^2+C1x+C2)e^(3x)
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