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 : Saturday, March 29, 2025 at 10:53:19 PM
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*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
u = Function("u") 
ode = Eq(u(t)**3/5 - cos(t) + Derivative(u(t), t) + Derivative(u(t), (t, 2)),0) 
ics = {u(0): 2, Subs(Derivative(u(t), t), t, 0): 0} 
dsolve(ode,func=u(t),ics=ics)
 

NotImplementedError : solve: Cannot solve u(t)**3/5 - cos(t) + Derivative(u(t), t) + Derivative(u(t), (t, 2))