Internal problem ID [9240]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1661.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {8 y^{\prime \prime }+9 \left (y^{\prime }\right )^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 51
dsolve(8*diff(diff(y(x),x),x)+9*diff(y(x),x)^4=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (x +c_{1}\right )^{\frac {2}{3}}+c_{2} \\ y \relax (x ) = -\frac {\left (x +c_{1}\right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right )}{2}+c_{2} \\ y \relax (x ) = \frac {\left (x +c_{1}\right )^{\frac {2}{3}} \left (i \sqrt {3}-1\right )}{2}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 90
DSolve[9*y'[x]^4 + 8*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {1}{3} \sqrt [3]{-\frac {1}{3}} (9 x-8 c_1){}^{2/3} \\ y(x)\to \frac {(9 x-8 c_1){}^{2/3}}{3 \sqrt [3]{3}}+c_2 \\ y(x)\to \frac {1}{9} \left ((-3)^{2/3} (9 x-8 c_1){}^{2/3}+9 c_2\right ) \\ \end{align*}