Internal problem ID [14164]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }=-\frac {6}{t^{9}}+\frac {6}{t^{3}}-t^{7}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ \frac {t^{8}}{8}+\frac {3}{t^{2}}-\frac {3}{4 t^{8}}-\frac {4 s \left (t \right )^{9}}{9}+9 s \left (t \right )-\frac {1}{s \left (t \right )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 17.496 (sec). Leaf size: 531
DSolve[(6/t^9-6/t^3+t^7)+(9+1/s[t]^2-4*s[t]^8)*s'[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*}