74.1.4 problem 5

Internal problem ID [15784]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 08:07:09 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.104 (sec). Leaf size: 17

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

\begin{align*} y &= 0 \\ y &= -\frac {\left (x -c_{1} \right )^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 42

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

\begin{align*} y(x)\to -\frac {1}{4} (x+i c_1){}^2 \\ y(x)\to -\frac {1}{4} (x-i c_1){}^2 \\ y(x)\to 0 \\ \end{align*}