求微分方程特解
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求微分方程特解
x*dy/dx = ylny
dy/(ylny) = dx/x
lnlny = lnx + A
lny = x * e^A = B * x
y = e^(B*x) = (e^B)^x = C^x
由x=1时y=2,
C = 2
故特解是 y = 2^x
求微分方程特解
x*dy/dx = ylny
dy/(ylny) = dx/x
lnlny = lnx + A
lny = x * e^A = B * x
y = e^(B*x) = (e^B)^x = C^x
由x=1时y=2,
C = 2
故特解是 y = 2^x