73.8.27 problem 13.5 (c)

Internal problem ID [15235]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.5 (c)
Date solved : Tuesday, January 28, 2025 at 07:50:33 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]

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

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 40

dsolve(diff(y(x),x)*diff(y(x),x$2)=1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 49

DSolve[D[y[x],x]*D[y[x],{x,2}]==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_2-\frac {2}{3} \sqrt {2} (x+c_1){}^{3/2} \\ y(x)\to \frac {2}{3} \sqrt {2} (x+c_1){}^{3/2}+c_2 \\ \end{align*}