68.8.10 problem 10
Internal
problem
ID
[17433]
Book
:
INTRODUCTORY
DIFFERENTIAL
EQUATIONS.
Martha
L.
Abell,
James
P.
Braselton.
Fourth
edition
2014.
ElScAe.
2014
Section
:
Chapter
2.
First
Order
Equations.
Review
exercises,
page
80
Problem
number
:
10
Date
solved
:
Thursday, October 02, 2025 at 02:20:53 PM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
\begin{align*} 3 t +\left (t -4 y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.030 (sec). Leaf size: 47
ode:=3*t+(t-4*y(t))*diff(y(t),t) = 0;
dsolve(ode,y(t), singsol=all);
\[
y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{7} t^{2} c_1^{2} \left (t c_1 \right )^{{1}/{3}}-7 \textit {\_Z}^{4} t^{2} c_1^{2} \left (t c_1 \right )^{{1}/{3}}-4\right )^{3} t}{4}-\frac {3 t}{4}
\]
✓ Mathematica. Time used: 4.528 (sec). Leaf size: 477
ode=3*t+(t-4*y[t])*D[y[t],t]==0;
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\begin{align*} y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,1\right ]\\ y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,2\right ]\\ y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,3\right ]\\ y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,4\right ]\\ y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,5\right ]\\ y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,6\right ]\\ y(t)&\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,7\right ] \end{align*}
✓ Sympy. Time used: 0.449 (sec). Leaf size: 27
from sympy import *
t = symbols("t")
y = Function("y")
ode = Eq(3*t + (t - 4*y(t))*Derivative(y(t), t),0)
ics = {}
dsolve(ode,func=y(t),ics=ics)
\[
\log {\left (t \right )} = C_{1} - \log {\left (\left (-1 + \frac {y{\left (t \right )}}{t}\right )^{\frac {3}{7}} \left (\frac {3}{4} + \frac {y{\left (t \right )}}{t}\right )^{\frac {4}{7}} \right )}
\]