求微分方程的通解dy/dx-2y/(x+1)=(x+1)^5/2

对应的齐次方程为dy/dx-2y/(x+1)=0dy/y=2dx/(x+1)ln|y|=2ln|x+1|+ln|C1|y=C1(x+1)²用常数变易法,把C1换成u,即令y=u(x+1)² ①那么 dy/dx=u '(x+1)²+2u(x+1)代入所给非齐次方程,得u '=(x+1)^(1/2)两端...