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求下列非齐次线性微分方程的通解或在给定初始条件下的特解: (1)y〞-2yˊ+2y=x2; (2)y〞-3yˊ=-6x+2; (3)y〞+a2y=8cosbx,a,b≠0,a2≠b2; (4)2y〞+yˊ-y=3ex; (5)y〞+4yˊ+4y=8(x+e2x); (6)y〞+y=excosx,y(π/2)=0,yˊ(π/2)=0; (7)y〞-(α+β)yˊ+αβy=aeαx,其中α,β,a为常数; (8)y〞-6yˊ+25y=2sinx+3cosx, y(0)=1/2,yˊ(0)=1.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAYAAABzenr0AAAA5ElEQVRYR2NkGGDAOMD2M+B0wKpVq9huv/jbxPD/fxwDA4MkhQ59zsDIuEhVgrkuLCzsF7JZOB3QOml5B8P//+UUWoyqnZGxszovsoI4B0xc9gyfzxmZmb2rcsK3IRvWMWm599///7fgcfTz6vwoKWId8B+f75kZGX0q8iK3kugAhur8KJRQxx0FE5fhdQC5UTPqgNEQGA2B0RAYDYHREBgNgaETAuTW96TqG7yt4tbRFhGRIQBqHTP9+8dIoDUMTxqk5AK8zXKYiaDWMYhNpANIaJYPdMdkwLtmpOZnctUPeDkAAP6tmiH1ggTLAAAAAElFTkSuQmCC)
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