68.7.53 problem 58

Internal problem ID [17417]
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 : 58
Date solved : Thursday, October 02, 2025 at 02:18:35 PM
CAS classification : [_dAlembert]

\begin{align*} y&=-t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 32

ode:=y(t) = -t*diff(y(t),t)+1/5*diff(y(t),t)^5; 
dsolve(ode,y(t), singsol=all);
 

\[ \left [t \left (\textit {\_T} \right ) = \frac {\textit {\_T}^{{9}/{2}}+9 c_1}{9 \sqrt {\textit {\_T}}}, y \left (\textit {\_T} \right ) = \frac {4 \textit {\_T}^{5}}{45}-\sqrt {\textit {\_T}}\, c_1\right ] \]

✓ Mathematica. Time used: 1.163 (sec). Leaf size: 2076

ode=y[t]==-t*D[y[t],t]+1/5*D[y[t],t]^5; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) + y(t) - Derivative(y(t), t)**5/5,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE t*Derivative(y(t), t) + y(t) - Derivative(y(t), t)**5/5 cannot be solved by the lie group method