76.16.8 problem 23

Internal problem ID [17685]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.6 (Forced vibrations, Frequency response, and Resonance). Problems at page 272
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 10:59:31 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✗ Solution by Maple

dsolve([diff(y(t),t$2)+y(t)+2/10*y(t)^3=cos(w*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[t],{t,2}]+y[t]+2/10*y[t]^3==Cos[w*t],{y[0]==0,Derivative[1][y][0] == 0}},y[t],t,IncludeSingularSolutions -> True]
 

Not solved