Internal problem ID [12596]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises page 14
Problem number: 37.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}=x^{6}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2=x^6,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{4}}{4}+c_{1} \\ y \left (x \right ) &= -\frac {x^{4}}{4}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[(y'[x])^2==x^6,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^4}{4}+c_1 \\ y(x)\to \frac {x^4}{4}+c_1 \\ \end{align*}