Internal problem ID [8114]
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]
Solve \begin {gather*} \boxed {4 x \left (y^{\prime }\right )^{3}-6 y \left (y^{\prime }\right )^{2}+3 y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.346 (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 \relax (x ) = x \\ y \relax (x ) = \frac {\left (\frac {\left (c_{1}+x \right ) \sqrt {2}\, \sqrt {c_{1} \left (c_{1}+x \right )}}{c_{1}^{2}}+1\right ) x}{-\frac {3 \left (c_{1}+x \right )}{c_{1}}+3} \\ y \relax (x ) = \frac {\left (-\frac {\left (c_{1}+x \right ) \sqrt {2}\, \sqrt {c_{1} \left (c_{1}+x \right )}}{c_{1}^{2}}+1\right ) x}{-\frac {3 \left (c_{1}+x \right )}{c_{1}}+3} \\ y \relax (x ) = c_{1} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.651 (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 {\sqrt {2} \sqrt {c_1 (x+c_1){}^3}}{3 c_1}-\frac {c_1}{3} \\ y(x)\to \text {Indeterminate} \\ \end{align*}