48.1.15 problem Example 3.16

Internal problem ID [7516]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.16
Date solved : Monday, January 27, 2025 at 03:04:14 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

\begin{align*} y &= x^{2}+c_{1} \\ y &= -x^{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 23

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

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