Internal problem ID [1921]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{2} \left (y^{\prime } y-x \right )=-x^{3}} \]
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 50
dsolve(y(x)^2*(y(x)*diff(y(x),x)-x)+x^3=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (2 \textit {\_Z}^{2}+\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (\frac {3 \tan \left (\textit {\_Z} \right )^{2} x^{4}}{4}+\frac {3 x^{4}}{4}\right )+4 \sqrt {3}\, c_{1} -2 \textit {\_Z} \right )\right )-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 63
DSolve[y[x]^2*(y[x]*y'[x]-x)+x^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\arctan \left (\frac {\frac {2 y(x)^2}{x^2}-1}{\sqrt {3}}\right )}{2 \sqrt {3}}+\frac {1}{4} \log \left (\frac {y(x)^4}{x^4}-\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]