67.6.7 problem 7.4 (e)

Internal problem ID [16433]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.4 (e)
Date solved : Thursday, October 02, 2025 at 01:31:46 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} 4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 23

ode:=4*x^3*y(x)+(x^4-y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (-5 x^{4} c_1^{4} \textit {\_Z} +\textit {\_Z}^{5}-1\right )}{c_1} \]

✓ Mathematica. Time used: 1.359 (sec). Leaf size: 131

ode=4*x^3*y[x]+(x^4-y[x]^4)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1} x^4+e^{5 c_1}\&,5\right ]\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.397 (sec). Leaf size: 22

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

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\sqrt [5]{\frac {5 x^{4}}{y^{4}{\left (x \right )}} - 1} \right )} \]