Peano’s theorem

\displaystyle\frac{dy}{dx}

\displaystyle=

\displaystyle f(x,y)

(1)

is an ordinary differential equation where $f(x,y)$ is continuous on a planar domain $E$ , then (1) has at least one integral curve for each $(x_{0},y_{0})$ of $E$ .[KF, T]

References

KF Kolmogorov, A.N. & Fomin, S.V., Introductory Real Analysis, Translated & Edited by Richard A. Silverman, Dover Publications, Inc. New York, 1970.
T Teschl, Gerald, http://www.mat.univie.ac.at/ gerald/ftp/book-ode/index.htmlhttp://www.mat.univie.ac.at/ gerald/ftp/book-ode/index.html, 2004.