49.23.5 problem 1(e)

Internal problem ID [7763]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 238
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:12:15 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 23

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

\[ y = \frac {\tan \left (\frac {\left (x +c_{2} \right ) \sqrt {2}}{2 c_{1}}\right ) \sqrt {2}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 19.203 (sec). Leaf size: 34

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

\[ y(x)\to \sqrt {2} \sqrt {c_1} \tan \left (\frac {\sqrt {c_1} (x+c_2)}{\sqrt {2}}\right ) \]