19.3.6 problem 14

Internal problem ID [3549]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:42:36 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(x*(x^2-y(x)^2)-x*(x^2+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}+1}{\textit {\_a}^{3}+\textit {\_a}^{2}+\textit {\_a} -1}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 71

DSolve[x*(x^2-y[x]^2)-x*(x^2+y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}-1\&,\frac {\text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+2 \text {$\#$1}+1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]