60.7.164 problem 1755 (book 6.164)

Internal problem ID [11753]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1755 (book 6.164)
Date solved : Monday, January 27, 2025 at 11:34:10 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 19

dsolve(n*y(x)*diff(diff(y(x),x),x)-(n-1)*diff(y(x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \left (\frac {c_{1} x +c_{2}}{n}\right )^{n} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.527 (sec). Leaf size: 17

DSolve[(1 - n)*D[y[x],x]^2 + n*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 (x-c_1 n){}^n \]