Question

这个怎么求出来的，看不懂！微分方程的题

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Answer 1

u=[f(x)]^(-1/2)

du/dx = -(1/2)[f(x)]^(-3/2) . f'(x)
= -(1/2) u^3 . f'(x)
f'(x)= -(2/u^3). du/dx
/

f'(x) +(2/x)f(x) = [2/(ax)][f(x)]^(3/2)
-(2/u^3). du/dx + (2/x)(1/u^2) = [2/(ax)] (1/u^3)
-(1/u). du/dx + 1/x = [1/(ax)] (1/u)
du/dx - (1/x)u = -1/(ax)