Internal problem ID [5095]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-4 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(diff(y(x),x)^2=4*x^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = x^{2}+c_{1} \\ y \relax (x ) = -x^{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[(y'[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*}