60.1.459 problem 462

Internal problem ID [10473]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 462
Date solved : Monday, January 27, 2025 at 07:54:40 PM
CAS classification : [_quadrature]

\begin{align*} y {y^{\prime }}^{2}-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 27

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

\begin{align*} x -\frac {2 y^{{3}/{2}}}{3}-c_{1} &= 0 \\ x +\frac {2 y^{{3}/{2}}}{3}-c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 43

DSolve[-1 + y[x]*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (\frac {3}{2}\right )^{2/3} (-x+c_1){}^{2/3} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} (x+c_1){}^{2/3} \\ \end{align*}