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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2014 • Question 6

Question

Math 6410 • ODE Fall 2014 • Question 6

Show that for small \(\norm {\epsilon }\), there is a \(2\pi \)-periodic solution near zero to the inhomogeneous equation \[ \ddot {y}+5y=\epsilon \sin ^3 t. \]

Raw LaTeX

Show that for small \(\norm{\epsilon}\), there is a \(2\pi\)-periodic solution near zero
to the inhomogeneous equation
\[
  \ddot{y}+5y=\epsilon\sin^3 t.
\]

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Periodic Orbits, Limit Cycles, and Orbital Stability Poincare Maps and Periodic Solutions