Question

高数求助！

高数求助！第五题，A项为嘛不对

Answer 1

(3) let u=y/x^4 du/dx = (1/x^4). dy/dx - 4y/x^5 dy/dx = x^4.[ du/dx + (4/x)u] --------- dy/dx - (4/x)y = x√y x^4.[ du/dx + (4/x)u] - (4/x^3)u = x^3.√u x^4. du/dx =x^3.√u x.du/dx =√u ∫ du/√u = ∫ dx/x 2√u = ln|x| +C' 2√y/x^2 = ln|x| +C' y = (1/4) x^4 . ( ln|Cx| )^2 (6) f(x) - ∫(0->x) (x-u) f(u) du = x+3 f(x) -x ∫(0->x) f(u) du +∫(0->x) uf(u) du = x+3 两边取导数 f'(x) -∫(0->x) f(u) du - xf(x) +xf(x) = 1 f'(x) -∫(0->x) f(u) du = 1 两边取导数 f''(x) - f(x) =0 The aux. equation p^2 -1 =0 p=1 or -1 let f(x)= Ae^x +Be^(-x) f(0) =3 A+B=3 (1) f'(0)=1 A-B = 1 (2) (1)+(2) A= 2 from (1) B= 1 ie f(x) = 2e^x +e^(-x)

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