74.7.57 problem 64

Internal problem ID [16063]
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 : 64
Date solved : Monday, March 31, 2025 at 02:37:32 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 171

ode:=t^(1/3)*y(t)^(2/3)+t+(t^(2/3)*y(t)^(1/3)+y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ -\int _{\textit {\_b}}^{t}\frac {y^{{8}/{3}} \textit {\_a}^{{1}/{3}}-y^{{4}/{3}} \textit {\_a}^{{5}/{3}}+\textit {\_a}^{3}}{\textit {\_a}^{4}+y^{4}}d \textit {\_a} -\frac {\int _{}^{y}\frac {\left (4 t^{2}+4 \textit {\_f}^{{2}/{3}} t^{{4}/{3}}+4 \textit {\_f}^{{4}/{3}} t^{{2}/{3}}+4 \textit {\_f}^{2}\right ) \int _{\textit {\_b}}^{t}\frac {\textit {\_f}^{{17}/{3}} \textit {\_a}^{{1}/{3}}-2 \textit {\_f}^{{13}/{3}} \textit {\_a}^{{5}/{3}}-2 \textit {\_f}^{{5}/{3}} \textit {\_a}^{{13}/{3}}+\textit {\_f}^{{1}/{3}} \textit {\_a}^{{17}/{3}}+3 \textit {\_a}^{3} \textit {\_f}^{3}}{\left (\textit {\_a}^{4}+\textit {\_f}^{4}\right )^{2}}d \textit {\_a} +3 t^{{2}/{3}} \textit {\_f}^{{1}/{3}}+3 \textit {\_f}}{\textit {\_f}^{{4}/{3}} t^{{2}/{3}}+\textit {\_f}^{{2}/{3}} t^{{4}/{3}}+t^{2}+\textit {\_f}^{2}}d \textit {\_f}}{3}+c_1 = 0 \]

✓ Mathematica. Time used: 1.793 (sec). Leaf size: 53

ode=(t^(1/3)*y[t]^(2/3)+t)+(t^(2/3)*y[t]^(1/3)+y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \left (-t^{2/3}\right )^{3/2} \\ y(t)\to \left (-t^{4/3}+\frac {4 c_1}{3}\right ){}^{3/4} \\ y(t)\to \left (-t^{2/3}\right )^{3/2} \\ \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**(1/3)*y(t)**(2/3) + t + (t**(2/3)*y(t)**(1/3) + y(t))*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out