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: 0.094 (sec). Leaf size: 102
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 ) = \left (-\frac {1}{2}-\frac {\sqrt {3}}{2}\right ) x y \left (x \right ) = \left (\frac {\sqrt {3}}{2}-\frac {1}{2}\right ) x y \left (x \right ) = x y \left (x \right ) = \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 \left (x \right ) = \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} \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*}