討論串[理工] [工數]-O.D.E.
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2. 2.解 xy'-4x y+2y(ln y)=0 , x≧1, y(1)=1. 令 u=ln(y), y=exp(u),y'=exp(u)*u'. 原式可化簡為 xu'-4x^2+2u=0. u'+(2/x)u=4x. integrator factor= x^2. 解出 u=x^2+c1*x^
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let x-1 = exp^t , t = ln(x-1) , D=d/dt. [D(D-1) + 4D + 2 ]y = 1. [D^2+3D+2]y = 1. yh = c1exp^(-t) + c2exp^(-2t). yp = 1/2. y = yh + yp = c1exp^(-t) +
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[解一]. y' = (-c1 sint + c2 cost) + (c1' cost + c2' sint). ^^^^^^^^^^^^^^^^^^^^^ = 0. y'' = (-c1 cost - c2 sint) + (-c1'sint +c2' cost). 代回微分方程式. c1'sin
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