求方程dy/dx-2y/x+1=(x+1)^5/2满足 y|x=0=1的特解
问题描述：
求方程dy/dx-2y/x+1=(x+1)^5/2满足 y|x=0=1的特解
答
∵dy/dx-2y/(x+1)=(x+1)^5/2==>2y/(x+1)=y'-(x+1)^5/2==>2y=(x+1)y'-(x+1)^6/2∴y=(x+1)y'/2-(x+1)^6/4令p=y',则y=(x+1)p/2-(x+1)^6/4.(1)设f(x,p)=(x+1)p/2-(x+1)^6/4∵f'x=p/2-3(x+1)^5/2,f'p=(x+1)/2 (f'x,f'p分...