Internal problem ID [8115]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 535.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {8 x \left (y^{\prime }\right )^{3}-12 y \left (y^{\prime }\right )^{2}+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 80
dsolve(8*x*diff(y(x),x)^3-12*y(x)*diff(y(x),x)^2+9*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {3 x}{2} \\ y \relax (x ) = \frac {3 x}{2} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (c_{1} \left (3 c_{1}+x \right )\right )^{\frac {3}{2}} x}{c_{1}^{3} \left (-\frac {3 \left (3 c_{1}+x \right )}{c_{1}}+9\right )} \\ y \relax (x ) = -\frac {\left (c_{1} \left (3 c_{1}+x \right )\right )^{\frac {3}{2}} x}{c_{1}^{3} \left (-\frac {3 \left (3 c_{1}+x \right )}{c_{1}}+9\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.271 (sec). Leaf size: 77
DSolve[9*y[x] - 12*y[x]*y'[x]^2 + 8*x*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}} \\ y(x)\to \frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}} \\ y(x)\to 0 \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\frac {3 x}{2} \\ y(x)\to \frac {3 x}{2} \\ \end{align*}