50.7.1 problem 1(a)

Internal problem ID [7905]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page 38
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:31:47 PM
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: 0.016 (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: 0.177 (sec). Leaf size: 20

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

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