Internal problem ID [3223]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 81.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 37
dsolve(y(x)=x*diff(y(x),x)+(diff(y(x),x))^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2 \sqrt {3}\, \left (-x \right )^{\frac {3}{2}}}{9} \\ y \left (x \right ) &= -\frac {2 \sqrt {3}\, \left (-x \right )^{\frac {3}{2}}}{9} \\ y \left (x \right ) &= c_{1} \left (c_{1}^{2}+x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 54
DSolve[y[x]==x*y'[x]+(y'[x])^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+c_1{}^2\right ) \\ y(x)\to -\frac {2 i x^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 i x^{3/2}}{3 \sqrt {3}} \\ \end{align*}