Internal problem ID [9419]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1844.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime } y^{2}-18 y^{\prime } y^{\prime \prime } y+15 \left (y^{\prime }\right )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 79
dsolve(4*y(x)^2*diff(diff(diff(y(x),x),x),x)-18*y(x)*diff(y(x),x)*diff(diff(y(x),x),x)+15*diff(y(x),x)^3=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 \\ y \left (x \right ) = {\mathrm e}^{\int \operatorname {RootOf}\left (-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_h}^{2}+\sqrt {c_{1} \textit {\_h}^{2}+c_{1}^{2}}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}} \\ y \left (x \right ) = {\mathrm e}^{\int \operatorname {RootOf}\left (2 \left (\int _{}^{\textit {\_Z}}-\frac {1}{\textit {\_h}^{2}-\sqrt {c_{1} \left (\textit {\_h}^{2}+c_{1} \right )}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 19
DSolve[15*y'[x]^3 - 18*y[x]*y'[x]*y''[x] + 4*y[x]^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{(x (c_3 x+c_2)+c_1){}^2} \\ \end{align*}