44.1.4 problem 4

Internal problem ID [6879]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 02:47:35 AM
CAS classification : [NONE]

\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \end{align*}

✗ Maple

ode:=diff(diff(u(r),r),r)+diff(u(r),r)+u(r) = cos(r+u(r)); 
dsolve(ode,u(r), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[u[r],{r,2}]+D[u[r],r]+u[r]==Cos[r+u[r]]; 
ic={}; 
DSolve[{ode,ic},u[r],r,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
r = symbols("r") 
u = Function("u") 
ode = Eq(u(r) - cos(r + u(r)) + Derivative(u(r), r) + Derivative(u(r), (r, 2)),0) 
ics = {} 
dsolve(ode,func=u(r),ics=ics)
 

NotImplementedError : solve: Cannot solve u(r) - cos(r + u(r)) + Derivative(u(r), r) + Derivative(u(r), (r, 2))