y'=cos(x-y)-cos(x+y)的通解,求详解.

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 08:09:55
y'=cos(x-y)-cos(x+y)的通解,求详解.

y'=cos(x-y)-cos(x+y)的通解,求详解.
y'=cos(x-y)-cos(x+y)的通解,求详解.

y'=cos(x-y)-cos(x+y)的通解,求详解.
∵y'=cos(x-y)-cos(x+y)
==>y'=(cosxcosy+sinxsiny)-(cosxcosy-sinxsiny) (应用余弦和差角公式)
==>y'=2sinxsiny
==>dy/siny=sinxdx
==>∫[1/(cosy-1)-1/(cosy+1)]d(cosy)=2∫sinxdx
==>ln│(cosy-1)/(cosy+1)│=-2cosx+ln│C│ (C是积分常数)
==>(cosy-1)/(cosy+1)=Ce^(-2cosx)
==>cosy=[1+Ce^(-2cosx)]/[1-Ce^(-2cosx)]
∴原方程的通解是cosy=[1+Ce^(-2cosx)]/[1-Ce^(-2cosx)] (C是积分常数).

y'=(cosxcosy+sinxsiny)-(cosxcosy-sinxsiny)=2sinxsiny
y=-2sinxcosy

：y' +y= cos x y= cos(x)看到这个 cos(x)－cos(y)=? 证明COS（X+Y）COS（X-Y）=COS^2X-SIN^2Y 证明cos(x+y)cos(x-y)= cos^2(x)-sin^2(y) 求解微分方程y+y=cos x y=2cos x (sin x+cos x) 解微分方程y'=y/x+cos(y/x) 解微分方程y'=y/x+cos(y/x) y=cos(x+y) y对x的导数y=cos（x+y) y对x的导数 y=(sin x + COS x)^2 y=(cos x-2)/(cos x-1)的值域 sin(x+y)sin(x-y)=k,求cos^2x-cos^2y y=cos^2 x-cos x +1的值域y=cos^2 x+cos x +1的值域, cos(x+y)*cos(x-y)=cos*cosx+sin*siny 求解微分方程y'*cos(y)=x+1-sin(y) 解微分方程：y` cos y =(1+cos x sin y)sin y. 2cos(x+y)cosx-cos(2x+y)化简 公式cos(x+y)等于?