Internal problem ID [1964]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\[ \boxed {\frac {x^{2}-y^{2}}{x \left (y^{2}+2 x^{2}\right )}+\frac {\left (2 y^{2}+x^{2}\right ) y^{\prime }}{y \left (y^{2}+2 x^{2}\right )}=0} \]
✓ Solution by Maple
Time used: 6.063 (sec). Leaf size: 33
dsolve((x^2-y(x)^2)/(x*(2*x^2+y(x)^2))+(x^2+2*y(x)^2)/(y(x)*(2*x^2+y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \operatorname {RootOf}\left (\textit {\_Z}^{16} c_{1}^{2}+2 x^{4} \textit {\_Z}^{4}-x^{4}\right )^{6}}{x} \]
✓ Solution by Mathematica
Time used: 60.251 (sec). Leaf size: 3381
DSolve[(x^2-y[x]^2)/(x*(2*x^2+y[x]^2))+(x^2+2*y[x]^2)/(y[x]*(2*x^2+y[x]^2))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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