Question

解微分方程:dy/dx–2y/（x+1）=（x+1）^5/2.求解

Answer 1

dy/dx–2y/（x+1）=（x+1）^5/2为一阶线性方程，由通解公式：
y=(x+1)^2(C+∫(x+1)^(1/2)dx)
=(x+1)^2(C+(2/3)(x+1)^(3/2))
=C(x+1)^2+(2/3)(x+1)^(7/2)