74.7.22 problem 22

Internal problem ID [16020]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 22
Date solved : Thursday, March 13, 2025 at 07:16:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {t +4 y}{4 t +y} \end{align*}

✓ Maple. Time used: 2.186 (sec). Leaf size: 36

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

\[ y = \left (\operatorname {RootOf}\left (\textit {\_Z}^{10} c_{1} t^{2}-\textit {\_Z}^{6}-6 \textit {\_Z}^{4}-12 \textit {\_Z}^{2}-8\right )^{2}+1\right ) t \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 40

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

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

✓ Sympy. Time used: 0.918 (sec). Leaf size: 26

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

\[ \log {\left (t \right )} = C_{1} + \log {\left (\frac {\left (1 + \frac {y{\left (t \right )}}{t}\right )^{\frac {3}{2}}}{\left (-1 + \frac {y{\left (t \right )}}{t}\right )^{\frac {5}{2}}} \right )} \]