73.6.7 problem 7.4 (e)

Internal problem ID [15146]
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 : Tuesday, January 28, 2025 at 07:36:50 AM
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*}

✓ Solution by Maple

Time used: 0.286 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 50

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {(K[1]-1) (K[1]+1) \left (K[1]^2+1\right )}{K[1] \left (K[1]^4-5\right )}dK[1]=-\log (x)+c_1,y(x)\right ] \]