85.1.18 problem 11 (d)

Internal problem ID [22423]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 11 (d)
Date solved : Thursday, October 02, 2025 at 08:39:11 PM
CAS classification : [_quadrature]

\begin{align*} s^{\prime }&=9 \sqrt {u} \end{align*}

With initial conditions

\begin{align*} s \left (4\right )&=16 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 11

ode:=diff(s(u),u) = 9*u^(1/2); 
ic:=[s(4) = 16]; 
dsolve([ode,op(ic)],s(u), singsol=all);
 

\[ s = 6 u^{{3}/{2}}-32 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

ode=D[s[u],{u,1}]==9*Sqrt[u]; 
ic={s[4]==16}; 
DSolve[{ode,ic},s[u],u,IncludeSingularSolutions->True]
 

\begin{align*} s(u)&\to 6 u^{3/2}-32 \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 10

from sympy import * 
u = symbols("u") 
s = Function("s") 
ode = Eq(-9*sqrt(u) + Derivative(s(u), u),0) 
ics = {s(4): 16} 
dsolve(ode,func=s(u),ics=ics)
 

\[ s{\left (u \right )} = 6 u^{\frac {3}{2}} - 32 \]