85.33.83 problem 84

Internal problem ID [22706]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 84
Date solved : Thursday, October 02, 2025 at 09:11:15 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \end{align*}

With initial conditions

\begin{align*} u \left (1\right )&=15 \\ u^{\prime }\left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 18

ode:=diff(diff(u(r),r),r)+1/r*diff(u(r),r) = 4-4*r; 
ic:=[u(1) = 15, D(u)(1) = 0]; 
dsolve([ode,op(ic)],u(r), singsol=all);
 

\[ u = -\frac {4 r^{3}}{9}+r^{2}-\frac {2 \ln \left (r \right )}{3}+\frac {130}{9} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 25

ode=D[u[r],{r,2}]+1/r*D[u[r],r]==4*(1-r); 
ic={u[1]==15,Derivative[1][u][1] ==0}; 
DSolve[{ode,ic},u[r],r,IncludeSingularSolutions->True]
 

\begin{align*} u(r)&\to \frac {1}{9} \left (-4 r^3+9 r^2-6 \log (r)+130\right ) \end{align*}

✗ Sympy

from sympy import * 
r = symbols("r") 
u = Function("u") 
ode = Eq(4*r + Derivative(u(r), (r, 2)) - 4 + Derivative(u(r), r)/r,0) 
ics = {u(1): 15, Subs(Derivative(r(u), u), u, 1): 0} 
dsolve(ode,func=u(r),ics=ics)
 

ValueError : Invalid boundary conditions for Derivatives