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[单选题]
一阶线性非齐次微分万栏y'=p(x)y+q(x)的通解是( ).
A.y=e-∫p(x)dx[∫q(x)e∫p(x)dxdx+C]
B.y=e∫p(x)dx∫q(x)e∫p(x)dxdx;
C.y=e∫p(x)dx[∫q(x)e-∫p(x)dxdx+C];
D.y=Ce-∫p(x)dx
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A.y=e-∫p(x)dx[∫q(x)e∫p(x)dxdx+C]
B.y=e∫p(x)dx∫q(x)e∫p(x)dxdx;
C.y=e∫p(x)dx[∫q(x)e-∫p(x)dxdx+C];
D.y=Ce-∫p(x)dx
A.λ=1/2,μ=1/2
B.λ=-1/2,μ=-1/2
C.λ=2/3,μ=1/3
D.λ=2/3,μ=2/3
试证非齐次线性微分方程组的叠加原理:设x1(t),x2(t)分别是方程组
①
②
的解,则x(t)=x1(t)+x2(t)是方程组③的解。
设y1,y2是二阶非齐次线性微分方程y''+P(x)y'+Q(x)y=F(x)的两个解, 则对应齐次方程y''+P(x)y'+Q(x)y=0的解为?
A.C[y1(x)-y2(x)]
B.y1(x)+C[y1(x)-y2(x)]
C.C[y1(x)+y2(x)]
D.y1(x)+C[y1(x)+y2(x)]
设有常系数齐次线性微分方程组,A为二阶常数矩阵,记p=-trA,q=detA,设p2+q2≠0,试证
(1)当p>0且q>0时,零解渐近稳定;
(2)当p>0且q=0;或p=0且q>0时,零解渐近稳定;
(3)其它情形下零解都不稳定.
已知y=1、y=x、y=x2是某二阶非齐次线性微分方程的三个解,则该方程的通解为______.