10.12.4 problem 24

Internal problem ID [1360]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.7 Forced Vibrations. page 217
Problem number : 24
Date solved : Monday, January 27, 2025 at 04:56:07 AM
CAS classification : [NONE]

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

With initial conditions

\begin{align*} u \left (0\right )&=2\\ u^{\prime }\left (0\right )&=0 \end{align*}

✗ Solution by Maple

dsolve([diff(u(t),t$2)+diff(u(t),t)+1/5*u(t)^3 = cos(t),u(0) = 2, D(u)(0) = 0],u(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{D[u[t],{t,2}]+D[u[t],t]+1/5*u[t]^3 ==3*Cos[t],{u[0]==0,Derivative[1][u][0]==0}},u[t],t,IncludeSingularSolutions -> True]
 

Not solved