Internal problem ID [1921]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{2} \left (y y^{\prime }-x \right )+x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 50
dsolve(y(x)^2*(y(x)*diff(y(x),x)-x)+x^3=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (2 \textit {\_Z}^{2}+\sqrt {3}\, \tan \left (\RootOf \left (\sqrt {3}\, \ln \left (\frac {3 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{4}}{4}+\frac {3 x^{4}}{4}\right )+4 \sqrt {3}\, c_{1}-2 \textit {\_Z} \right )\right )-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 63
DSolve[y[x]^2*(y[x]*y'[x]-x)+x^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\text {ArcTan}\left (\frac {\frac {2 y(x)^2}{x^2}-1}{\sqrt {3}}\right )}{2 \sqrt {3}}+\frac {1}{4} \log \left (\frac {y(x)^4}{x^4}-\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]