討論串[理工] [工數]-高階ode
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y^2(y'/y)' - y^2 y' = 0 , (y'/y)' - y' = 0 ,y'/y -y = c1. dy y. y' = y^2 + c1y , ___________ = dx ,1/c1 ln____________ = x + c2. y(c1+y) y+c1. let L{x
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2 2. 1. yy"-(y') -y y'=0. c1. ans: y= ----------------. c2exp(-c1x) -1. 2. x"-2x'+3y'+2y=4. 2y'-x'+3y=0 x(0)=y(0)=x'(0)=0. 10 t 1 -2t 7 2 t 1 -2t. ans
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dp. 令y' = p y' = p ──. dy. dp 2y. p [ ── - ──── ] = 0. p 1+y^2. p = 0 y = c 為trivial. 2. ln│p│ = ln│1+y│ +c1. dy 2. p = ── = c1(1+y ). dx. dy. ─── = c
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3t 2t. [ D(D-1) -4D +6 ]y = 2e +e. 2 3t 2t. [D -D -4D +6 ]y = 2e +e. mt. 令y=e. (m -3 ) (m-2) =0. 3t 2t 3 2. yh = c1e +c2e = c1x + c2x. 1 3t 2t 3t 2t 3
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