7.5.53 problem 53

Internal problem ID [157]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 53
Date solved : Friday, February 07, 2025 at 07:59:00 AM
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 y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.084 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 14.340 (sec). Leaf size: 24

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

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