Internal problem ID [2069]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (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)
\[ y \relax (x ) = \RootOf \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}+1}{\textit {\_a}^{3}+\textit {\_a}^{2}+\textit {\_a} -1}d \textit {\_a} +\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 71
DSolve[x*(x^2-y[x]^2)-x*(x^2+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}-1\&,\frac {\text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+2 \text {$\#$1}+1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]