用拉氏变换求微分方程+y+”-2y'-3y=+e+'满足初始条件+y+-。=-1,+y+-+o+=2的特
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亲你好，非常高兴为你解答，解：s2 Y(S)-sy(0)-y'(0)+2sY(S)-3Y(S)=1/(s+1)s2Y(S)-1+2sY(S)-3Y(S)=1/(s+1)Y(S)=(s+2)/(s2+2s-3)=(s+2)/[(s-3)(s+1)]=(5/4)/(s-3) + (-1/4)/(s+1)y(t)=(5/4)e3t +(-1/4)e-t
咨询记录 · 回答于2022-12-16
用拉氏变换求微分方程+y+”-2y'-3y=+e+'满足初始条件+y+-。=-1,+y+-+o+=2的特
亲你好，非常高兴为你解答，解：s2 Y(S)-sy(0)-y'(0)+2sY(S)-3Y(S)=1/(s+1)s2Y(S)-1+2sY(S)-3Y(S)=1/(s+1)Y(S)=(s+2)/(s2+2s-3)=(s+2)/[(s-3)(s+1)]=(5/4)/(s-3) + (-1/4)/(s+1)y(t)=(5/4)e3t +(-1/4)e-t
能不能发照片呢？这样不会写呀
y''+2y'-3y=0 y'(0)=1 y(0)=0取Laplace变换有[s^2Y(s)-sy(0)-y'(0)]+2[sY(s)-y(0)]-3Y(s)=0即s^2Y(s)-1+2sY(s)-3Y(s)=0Y(s)=1/(s^2+2s-3)=1/4[1/(s-1)-1/(s+3)]取逆变换有y(t)=1/4[e^(t)-e^(-3t)]
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