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# 第五节 全 微 分 方 程 - PowerPoint PPT Presentation

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## PowerPoint Slideshow about ' 第五节 全 微 分 方 程' - jermaine-alford

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u(x,y)=C就是全微分方程(1)的隐式通解,C是任意常数.

(2) 在区域G内恒成立,且当条件满足时,全微分方程

(1) 的通解为

1 求解 (5x4+3xy2-y3)dx+(3x2y-3xy2+y2)dy=0

y0=0. 根据公式(3),有

μ(x,y)p(x,y)dx+ μ(x,y)Q(x,y)dy=0

xy则方程可能有积分因子:

A.若方程中其他的项都只含有x或y的微分表达式,则方程

B.若方程中其他的项含有因式xy,则方程可能有积分因子

1/xy;

C.若方程中其他的项含有因式x2+ y2或x2-y2,则方程可

3 求微分方程 xdx+y(1+4y4+4x2y2)dy=0的通解

4 求微分方程 xdy+ydx+x2ydx+xy2dy=0的通解

xdy+ydx→d(xy),取积分因子1/xy