×

Integro-series solutions of linear ordinary differential systems with variable coefficients. (Chinese. English summary) Zbl 0790.34016

The author studies the linear system of differential equations \(\dot x=A(t) x+F(t)\). It is proved that the special solution \(x_ s(t)=\int^ t_{t_ 0} G(h\tau) F(\tau)d \tau\) can be expressed by the following series \[ x_ s(t)=\sum^ \infty_{\nu=0} (-1)^ \nu \sum^ \infty_{\lambda=0} P(\lambda,\nu) {(t-\overline t)^ \lambda \over \lambda!} F_{(\nu+1)}(t) \] where \(F_{(\nu+1)}(t)=\int^ t_{t_ 0} F_ \nu(s)ds\), \(\overline t\) is fixed and \(P\) is related to \(G\).
Reviewer: S.Hu (Springfield)

MSC:

34A30 Linear ordinary differential equations and systems
34A05 Explicit solutions, first integrals of ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
PDFBibTeX XMLCite