74.4.6 problem 6
Internal
problem
ID
[15899]
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
:
Tuesday, January 28, 2025 at 08:17:58 AM
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*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 36
dsolve((6/t^9-6/t^3+t^7)+(9+1/s(t)^2-4*s(t)^8)*diff(s(t),t)=0,s(t), singsol=all)
\[
\frac {t^{8}}{8}-\frac {3}{4 t^{8}}+\frac {3}{t^{2}}-\frac {4 s^{9}}{9}+9 s-\frac {1}{s}+c_{1} = 0
\]
✓ Solution by Mathematica
Time used: 16.875 (sec). Leaf size: 531
DSolve[(6/t^9-6/t^3+t^7)+(9+1/s[t]^2-4*s[t]^8)*D[s[t],t]==0,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*}