68.4.5 problem 5

Internal problem ID [17185]
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
Date solved : Thursday, October 02, 2025 at 01:49:46 PM
CAS classification : [_separable]

\begin{align*} 6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 23

ode:=6+4*t^3+(5+9/y(t)^8)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \frac {t^{4}}{2}+3 t +\frac {5 y}{2}-\frac {9}{14 y^{7}}+c_1 = 0 \]

✓ Mathematica. Time used: 3.551 (sec). Leaf size: 265

ode=(6+4*t^3)+(5+9/y[t]^8)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*t**3 + (5 + 9/y(t)**8)*Derivative(y(t), t) + 6,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ t^{4} + 6 t + 5 y{\left (t \right )} - \frac {9}{7 y^{7}{\left (t \right )}} = C_{1} \]