[理工] [工數]-變係數ODE
x^3y"-4xy'+4y=0
已知一解為x令y=vx y'=v'x+v y"=v"x+2v'
代入得到 x^2v"+2xv'-4v'=0
x^2dv'+(2x-4)v'dx=0
1 2x 4
──dv'+(─── - ──)dx=0
v' x^2 x^2
4
lnv' + lnx^2 + ── = c
x
4
v'=x^-2 e^(c- ──)
x
4
最後這v'要怎積分阿 答案是y=c1x+c2xe^(- ──)
x
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