7.5.44 problem 44

Internal problem ID [148]
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 : 44
Date solved : Friday, February 07, 2025 at 07:58:39 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 33

dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 20

DSolve[y[x]*D[y[x],{x,2}]+D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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