Internal problem ID [13728]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve(diff(y(x),x)^2+y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = -\frac {1}{4} x^{2}+\frac {1}{2} c_{1} x -\frac {1}{4} c_{1}^{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 42
DSolve[y'[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*}