32.10.1 problem Exercise 35.1, page 504

Internal problem ID [5995]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.1, page 504
Date solved : Monday, January 27, 2025 at 01:30:36 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 }&=2 y^{\prime } y \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 12.497 (sec). Leaf size: 24

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

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