74.4.6 problem 6

Internal problem ID [15828]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 6
Date solved : Monday, March 31, 2025 at 01:57:14 PM
CAS classification : [_separable]

\begin{align*} \frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 36

ode:=6/t^9-6/t^3+t^7+(9+1/s(t)^2-4*s(t)^8)*diff(s(t),t) = 0; 
dsolve(ode,s(t), singsol=all);
 

\[ \frac {t^{8}}{8}-\frac {3}{4 t^{8}}+\frac {3}{t^{2}}-\frac {4 s^{9}}{9}+9 s-\frac {1}{s}+c_1 = 0 \]

✓ Mathematica. Time used: 16.875 (sec). Leaf size: 531

ode=(6/t^9-6/t^3+t^7)+(9+1/s[t]^2-4*s[t]^8)*D[s[t],t]==0; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,1\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,2\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,3\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,4\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,5\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,6\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,7\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,8\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,9\right ] \\ s(t)\to \text {Root}\left [32 \text {$\#$1}^{10} t^8-648 \text {$\#$1}^2 t^8+\text {$\#$1} \left (-9 t^{16}-72 c_1 t^8-216 t^6+54\right )+72 t^8\&,10\right ] \\ \end{align*}

✓ Sympy. Time used: 0.389 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(t**7 + (-4*s(t)**8 + 9 + s(t)**(-2))*Derivative(s(t), t) - 6/t**3 + 6/t**9,0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

\[ - \frac {t^{8}}{8} + \frac {4 s^{9}{\left (t \right )}}{9} - 9 s{\left (t \right )} + \frac {1}{s{\left (t \right )}} - \frac {3 \left (4 t^{6} - 1\right )}{4 t^{8}} = C_{1} \]