7.5.54 problem 54

Internal problem ID [158]
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 : 54
Date solved : Friday, February 07, 2025 at 07:59:03 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }&=3 {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 33

dsolve(y(x)*diff(y(x),x$2)=3*diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \frac {1}{\sqrt {-2 c_1 x -2 c_2}} \\ y &= -\frac {1}{\sqrt {-2 c_1 x -2 c_2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 23

DSolve[y[x]*D[y[x],{x,2}]==3*D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_2}{\sqrt {2 x+c_1}} \\ y(x)\to 0 \\ \end{align*}