求微分方程 y✀=y⼀(x+y)+(x+y)^(3⼀2)的通解

2024-11-25 04:49:39
推荐回答(1个)
回答1:

设p=y'
则y"=dp/dx=dp/dy* dy/dx=pdp/dy
方程化为:pdp/dy=p^3+p
dp/dy=p^2+1
dp/(p^2+1)=dy
arctanp=y+c
p=tan(y+c)
dy/dx=tan(y+c)
dy/tan(y+c)=dx
cos(y+c)dy/sin(y+c)=dx
d(sin(y+c))/sin(y+c)=dx
ln[sin(y+c)]=x+c1
sin(y+c)=c2e^x