Internal problem ID [11803]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 12.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-9 y^{4}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2=9*y(x)^4,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{-3 x +c_{1}} y \left (x \right ) = \frac {1}{3 x +c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.263 (sec). Leaf size: 34
DSolve[y'[x]^2==9*y[x]^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3 x+c_1} y(x)\to \frac {1}{3 x-c_1} y(x)\to 0 \end{align*}