74.8.10 problem 10

Internal problem ID [16075]
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 : Monday, March 31, 2025 at 02:38:52 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: 0.097 (sec). Leaf size: 45

ode:=3*t+(t-4*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t \left (\operatorname {RootOf}\left (\textit {\_Z}^{7} t^{2} c_1^{2} \left (t c_1 \right )^{{1}/{3}}-7 \textit {\_Z}^{4} t^{2} c_1^{2} \left (t c_1 \right )^{{1}/{3}}-4\right )^{3}-3\right )}{4} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 44

ode=3*t+(t-4*y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {4 K[1]-1}{(K[1]-1) (4 K[1]+3)}dK[1]=-\log (t)+c_1,y(t)\right ] \]

✓ Sympy. Time used: 0.681 (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)
 

\[ \log {\left (t \right )} = C_{1} - \log {\left (\left (-1 + \frac {y{\left (t \right )}}{t}\right )^{\frac {3}{7}} \left (\frac {3}{4} + \frac {y{\left (t \right )}}{t}\right )^{\frac {4}{7}} \right )} \]