76.5.35 problem 36

Internal problem ID [17384]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 36
Date solved : Monday, March 31, 2025 at 04:12:25 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y-y^{{1}/{4}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(y(x),x)+y(x)-y(x)^(1/4) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y^{{3}/{4}}-1-{\mathrm e}^{-\frac {3 x}{4}} c_1 = 0 \]

✓ Mathematica. Time used: 1.211 (sec). Leaf size: 33

ode=D[y[x],x]+y[x]-y[x]^(1/4)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \left (1+e^{-\frac {3}{4} (x-c_1)}\right ){}^{4/3} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**(1/4) + y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out