Internal problem ID [8869]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 534.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+3 y=x} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 84
dsolve(4*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+3*y(x)-x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\left (1+\sqrt {3}\right ) x}{2} \\ y \left (x \right ) &= \frac {\left (\sqrt {3}-1\right ) x}{2} \\ y \left (x \right ) &= x \\ y \left (x \right ) &= \frac {-\left (x +c_{1} \right ) \sqrt {2}\, \sqrt {c_{1} \left (x +c_{1} \right )}-c_{1}^{2}}{3 c_{1}} \\ y \left (x \right ) &= \frac {\left (x +c_{1} \right ) \sqrt {2}\, \sqrt {c_{1} \left (x +c_{1} \right )}-c_{1}^{2}}{3 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.143 (sec). Leaf size: 79
DSolve[-x + 3*y[x] - 6*y[x]*y'[x]^2 + 4*x*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2} \sqrt {c_1 (x+c_1){}^3}+c_1{}^2}{3 c_1} \\ y(x)\to -\frac {c_1{}^2-\sqrt {2} \sqrt {c_1 (x+c_1){}^3}}{3 c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}