求微分方程的通解.

解：1）求对应的齐次方程的通解：<br/><br/>&nbsp; &nbsp; 由特征方程<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/15892042395038946cf26971143f282b009b5546e88bdimage115.png" style="font-size: 14px; width: 106px; height: 23px;">得特征根为<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1589204239554e6fc0fe63d1149a985caa46a81877432image116.png" style="font-size: 14px; width: 101px; height: 26px;">，故通解为<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1589204239615d60d83c24ba94d2c98da954d4099a6f8image117.png" style="font-size: 14px; width: 151px; height: 30px;"><br/>2）求原方程的一个特解：<br/><br/>依题意设原方程的一个特解形式为<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/15892042396716aa99618d3224a099f1912b876208b00image118.png" style="font-size: 14px; width: 106px; height: 29px;"><br/>将<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/15892042397335542d1566a3148f8be07ec69e0320a42image119.png" style="font-size: 14px; width: 113px; height: 35px;">代入原方程中得到<br/><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1589204239783d33c85846e8648e7affa8075586bc916image120.png" style="width:121px;height:47px;">，<br/>所以，原方程的通解为<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/158920423982695940afeaf1a46318979e76f4abbb1c2image121.png" style="font-size: 14px; width: 349px; height: 46px;"><br/>
解：1）求对应的齐次方程的通解：    由特征方程得特征根为，故通解为2）求原方程的一个特解：依题意设原方程的一个特解形式为将代入原方程中得到，所以，原方程的通解为