44.3.20 problem 3(d)

Internal problem ID [9130]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 3(d)
Date solved : Tuesday, September 30, 2025 at 06:05:40 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 64

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

\begin{align*} y &= \frac {1}{\left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_1 +1\right )^{{1}/{3}}} \\ y &= -\frac {1+i \sqrt {3}}{2 \left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_1 +1\right )^{{1}/{3}}} \\ y &= \frac {i \sqrt {3}-1}{2 \left ({\mathrm e}^{\frac {3 x^{2}}{2}} c_1 +1\right )^{{1}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 76

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1] \left (K[1]^2+K[1]+1\right )}dK[1]\&\right ]\left [\frac {x^2}{2}+c_1\right ]\\ y(x)&\to 0\\ y(x)&\to 1\\ y(x)&\to -\sqrt [3]{-1}\\ y(x)&\to (-1)^{2/3} \end{align*}

✗ Sympy

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

Timed Out