用Laplace变换求解常微分方程:y'''-3y''+3y'-y=-1,y''(0)=y'(0)=1,y(0)=22、用Laplace变换求解常微分方程y'''+y'=e^2t满足初始条件y(0)=y'(0)=y''(0)=0的解小弟感激不尽
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![用Laplace变换求解常微分方程:y'''-3y''+3y'-y=-1,y''(0)=y'(0)=1,y(0)=22、用Laplace变换求解常微分方程y'''+y'=e^2t满足初始条件y(0)=y'(0)=y''(0)=0的解小弟感激不尽](/uploads/image/z/5409079-7-9.jpg?t=%E7%94%A8Laplace%E5%8F%98%E6%8D%A2%E6%B1%82%E8%A7%A3%E5%B8%B8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%EF%BC%9Ay%27%27%27-3y%27%27%2B3y%27-y%3D-1%2Cy%27%27%280%29%3Dy%27%280%29%3D1%2Cy%280%29%3D22%E3%80%81%E7%94%A8Laplace%E5%8F%98%E6%8D%A2%E6%B1%82%E8%A7%A3%E5%B8%B8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8By%27%27%27%2By%27%3De%5E2t%E6%BB%A1%E8%B6%B3%E5%88%9D%E5%A7%8B%E6%9D%A1%E4%BB%B6y%280%29%3Dy%27%280%29%3Dy%27%27%280%29%3D0%E7%9A%84%E8%A7%A3%E5%B0%8F%E5%BC%9F%E6%84%9F%E6%BF%80%E4%B8%8D%E5%B0%BD)
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用Laplace变换求解常微分方程:y'''-3y''+3y'-y=-1,y''(0)=y'(0)=1,y(0)=22、用Laplace变换求解常微分方程y'''+y'=e^2t满足初始条件y(0)=y'(0)=y''(0)=0的解小弟感激不尽
用Laplace变换求解常微分方程:y'''-3y''+3y'-y=-1,y''(0)=y'(0)=1,y(0)=2
2、用Laplace变换求解常微分方程y'''+y'=e^2t满足初始条件y(0)=y'(0)=y''(0)=0的解
小弟感激不尽
用Laplace变换求解常微分方程:y'''-3y''+3y'-y=-1,y''(0)=y'(0)=1,y(0)=22、用Laplace变换求解常微分方程y'''+y'=e^2t满足初始条件y(0)=y'(0)=y''(0)=0的解小弟感激不尽
令y=e^rx
代入得特征方程
r^3-3r^3+3r-1=0
r有三重实根r=1
所以y=e^x(c1+c2x+c3x^2)
边界条件得y=e^ x(2-x+1/2x^2)