60.7.71 problem 1662 (book 6.71)

Internal problem ID [11660]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1662 (book 6.71)
Date solved : Monday, January 27, 2025 at 11:29:38 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 8 y^{\prime \prime }+9 {y^{\prime }}^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 55

dsolve(8*diff(diff(y(x),x),x)+9*diff(y(x),x)^4=0,y(x), singsol=all)
 

\begin{align*} y &= \left (x +c_{1} \right )^{{2}/{3}}+c_{2} \\ y &= -\frac {i \sqrt {3}\, \left (x +c_{1} \right )^{{2}/{3}}}{2}-\frac {\left (x +c_{1} \right )^{{2}/{3}}}{2}+c_{2} \\ y &= \frac {i \sqrt {3}\, \left (x +c_{1} \right )^{{2}/{3}}}{2}-\frac {\left (x +c_{1} \right )^{{2}/{3}}}{2}+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 90

DSolve[9*D[y[x],x]^4 + 8*D[y[x],{x,2}] == 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*}