(xy'-y)cos^2(y/x)+x=0 求齐次方程的通解
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(xy''-y)cos^2(y/x)+x=0求齐次方程的通解(xy''-y)cos^2(y/x)+x=0求齐次方程的通解(xy''-y)cos^2(y/x)+x=0求齐次方程的通解令y=xuy''=u+xu''
(xy'-y)cos^2(y/x)+x=0 求齐次方程的通解
(xy'-y)cos^2(y/x)+x=0 求齐次方程的通解
(xy'-y)cos^2(y/x)+x=0 求齐次方程的通解
令y=xu
y'=u+xu'
代入原方程:
[x(u+xu')-xu]cos²u+x=0
xu'cos²u+1=0
cos²udu=-dx/x
(1+cos2u)du=-2dx/x
积分:u+0.5sin2u=-2ln|x|+C
即y/x+0.5sin(2y/x)=-2ln|x|+C
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