74.8.26 problem 26

Internal problem ID [16091]
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 : 26
Date solved : Monday, March 31, 2025 at 02:41:35 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=t y^{\prime }+3 {y^{\prime }}^{4} \end{align*}

✓ Maple. Time used: 0.106 (sec). Leaf size: 66

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

\begin{align*} y &= -\frac {18^{{1}/{3}} \left (-t \right )^{{4}/{3}}}{8} \\ y &= \frac {18^{{1}/{3}} \left (-t \right )^{{4}/{3}} \left (1+i \sqrt {3}\right )}{16} \\ y &= -\frac {18^{{1}/{3}} \left (-t \right )^{{4}/{3}} \left (i \sqrt {3}-1\right )}{16} \\ y &= c_1 \left (3 c_1^{3}+t \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 81

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

\begin{align*} y(t)\to c_1 \left (t+3 c_1{}^3\right ) \\ y(t)\to -\frac {1}{4} \left (-\frac {3}{2}\right )^{2/3} t^{4/3} \\ y(t)\to -\frac {1}{4} \left (\frac {3}{2}\right )^{2/3} t^{4/3} \\ y(t)\to \frac {1}{4} \sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} t^{4/3} \\ \end{align*}

✗ Sympy

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

Timed Out