y''=(y')^3+y' 求解微分方程的通解
问题描述：
y''=(y')^3+y' 求解微分方程的通解
答案是sin(y+C1)=C2e^x
求两种方法T.T
答
设p=y'则y"=dp/dx=dp/dy* dy/dx=pdp/dy方程化为：pdp/dy=p^3+pdp/dy=p^2+1dp/(p^2+1)=dyarctanp=y+cp=tan(y+c)dy/dx=tan(y+c)dy/tan(y+c)=dxcos(y+c)dy/sin(y+c)=dxd(sin(y+c))/sin(y+c)=dxln[sin(y+c)]=x+c1sin(y+c...