66.1.12 problem Problem 12

Internal problem ID [13859]
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
Date solved : Tuesday, January 28, 2025 at 06:05:42 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=9 y^{4} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 21

dsolve(diff(y(x),x)^2=9*y(x)^4,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{c_{1} -3 x} \\ y &= \frac {1}{3 x +c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 34

DSolve[D[y[x],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*}