44.1.43 problem 45

Internal problem ID [6918]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 45
Date solved : Monday, January 27, 2025 at 02:35:03 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 15

dsolve(diff(y(x),x)^2=4*y(x),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],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*}