35.7.6 problem 3

Internal problem ID [6188]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:47:08 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 17

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

\begin{align*} y &= 0 \\ y &= \frac {\left (c_1 x +c_2 \right )^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {(c_1 x+2 c_2){}^2}{4 c_2} \\ y(x)\to \text {Indeterminate} \\ \end{align*}