85.33.7 problem 7

Internal problem ID [22630]
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 : 7
Date solved : Thursday, October 02, 2025 at 08:56:56 PM
CAS classification : [_separable]

\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 77

ode:=s(t)^2*t*diff(s(t),t)+t^2+4 = 0; 
dsolve(ode,s(t), singsol=all);
 

\begin{align*} s &= \frac {\left (-12 t^{2}-96 \ln \left (t \right )+8 c_1 \right )^{{1}/{3}}}{2} \\ s &= -\frac {\left (-12 t^{2}-96 \ln \left (t \right )+8 c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ s &= \frac {\left (-12 t^{2}-96 \ln \left (t \right )+8 c_1 \right )^{{1}/{3}} \left (-1+i \sqrt {3}\right )}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 97

ode=s[t]^2*t*D[s[t],t]+(t^2+4)==0; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to -\sqrt [3]{-\frac {3}{2}} \sqrt [3]{-t^2-8 \log (t)+2 c_1}\\ s(t)&\to \sqrt [3]{\frac {3}{2}} \sqrt [3]{-t^2-8 \log (t)+2 c_1}\\ s(t)&\to (-1)^{2/3} \sqrt [3]{\frac {3}{2}} \sqrt [3]{-t^2-8 \log (t)+2 c_1} \end{align*}

✓ Sympy. Time used: 1.035 (sec). Leaf size: 78

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(t**2 + t*s(t)**2*Derivative(s(t), t) + 4,0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

\[ \left [ s{\left (t \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{C_{1} - \frac {3 t^{2}}{2} - 12 \log {\left (t \right )}}}{2}, \ s{\left (t \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{C_{1} - \frac {3 t^{2}}{2} - 12 \log {\left (t \right )}}}{2}, \ s{\left (t \right )} = \sqrt [3]{C_{1} - \frac {3 t^{2}}{2} - 12 \log {\left (t \right )}}\right ] \]