71.1.21 problem 35

Internal problem ID [14330]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 06:26:46 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 15

dsolve(diff(y(x),x)^2-4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 38

DSolve[(D[y[x],x])^2-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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