Internal problem ID [2358]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 39, page 179
Problem number: 27.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } x -\frac {3}{{y^{\prime }}^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 82
dsolve(y(x)=diff(y(x),x)*x+3/diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {3 \,6^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{2} y \left (x \right ) = -\frac {3 \,6^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-\frac {3 i \sqrt {3}\, 6^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4} y \left (x \right ) = -\frac {3 \,6^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}+\frac {3 i \sqrt {3}\, 6^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4} y \left (x \right ) = c_{1} x +\frac {3}{c_{1}^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 84
DSolve[y[x]==y'[x]*x+3/y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\frac {3}{c_1{}^2} y(x)\to -\frac {3 \sqrt [3]{-3} x^{2/3}}{2^{2/3}} y(x)\to \frac {3 \sqrt [3]{3} x^{2/3}}{2^{2/3}} y(x)\to \frac {3 (-1)^{2/3} \sqrt [3]{3} x^{2/3}}{2^{2/3}} \end{align*}