35.8.24 problem 24

Internal problem ID [6231]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 24
Date solved : Monday, January 27, 2025 at 01:49:32 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )&=y^{\prime } y \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 18

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

\[ y(x)\to c_2 \sqrt {x^2+c_1} \]