高等数学复习资料(3)

阶导数，limf(x)?1,求f(x)。

x??0????0???F?dS??????FdV????(f(x)?xf'(x)?xf(x)?e2x)dV 解：

s??112xexx(e?1) y'?(?1)y?e?y?xxx

第六讲 常微分方程

一、理论要求 1.一阶方程 2.高阶方程 3.二阶线性常系数

熟练掌握可分离变量、齐次、一阶线性、伯努利方程求法

会求y(n)?f(x),y''?f(x,y')(y'?p(x)),y''?f(y,y')(y'?p(y)) y''?py'?q?0??2?p??q?0??1??2?y1?c1e?1x?c2e?2x(齐次) ??x???1??2?y1?(c1?c2x)e??x????i??y?e(c1cos?x?c2sin?x)1?f(x)?Pn(x)e?x?????y2?Qn(x)e?x?(非齐次) ?????1or?2?y2?Qn(x)xe?x?2?x???and??y?Q(x)xe122n?f(x)?e?x(pi(x)cos?x?pj(x)sin?x)?x(非????i????y2?e(qn(x)cos?x?rn(x)sin?x???x????i????y2?xe(qn(x)cos?x?rn(x)sin?x(n?max(i,j)齐次)