Internal problem ID [2066]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 43
dsolve(y(x)*(3*x^2+y(x))-x*(x^2-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -\frac {x^{2} \left (\operatorname {RootOf}\left (\textit {\_Z}^{4} c_{1} -\textit {\_Z} c_{1} +3 x \right )^{3}-1\right )}{3 \operatorname {RootOf}\left (\textit {\_Z}^{4} c_{1} -\textit {\_Z} c_{1} +3 x \right )^{3}} \]
✓ Solution by Mathematica
Time used: 60.121 (sec). Leaf size: 1665
DSolve[y[x]*(3*x^2+y[x])-x*(x^2-y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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