Internal problem ID [13843]
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: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (5+\frac {9}{y^{8}}\right ) y^{\prime }=-4 t^{3}-6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((6+4*t^3)+(5+9/y(t)^8)*diff(y(t),t)=0,y(t), singsol=all)
\[ \frac {t^{4}}{2}+3 t +\frac {5 y}{2}-\frac {9}{14 y^{7}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.593 (sec). Leaf size: 265
DSolve[(6+4*t^3)+(5+9/y[t]^8)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,1\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,2\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,3\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,4\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,5\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,6\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,7\right ] y(t)\to \text {Root}\left [35 \text {$\#$1}^8+\text {$\#$1}^7 \left (7 t^4+42 t-7 c_1\right )-9\&,8\right ] \end{align*}