§12 ． 4 线性微分方程

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# §12 ． 4 线性微分方程 - PowerPoint PPT Presentation

§12 ． 4 线性微分方程. 一、线性方程. 齐次线性方程的解法. 线性方程、. 非齐次线性方程的解法. 二、伯努利方程. 伯努利方程、伯努利方程的解法：. 一、 线性方程. 线性方程：. 下列方程各是什么类型方程？. 方程. 叫做一阶线性微分方程． 如果 Q ( x )  0 ，则方程称为齐 次的，否则方程称为非齐次的．. 方程. 叫做对应于非齐次线性方程. 的齐次线性方程．. 齐次线性方程的解法：. 是变量可分离方程．分离变量得. 解 这是齐次线性方程，分 离变量得. 两边积分，得. 两边积分得

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§12．4 线性微分方程

ln|y|ln|x2|lnC，

yC(x2)．

（积分中不再加任意常数）．

ln y2ln (x1)ln C，

yC(x1)2．

R

i

L

~ E

K

(Em、w都是常数)，电阻R和电感L都是常量．求电流i(t)．