66.1.12 problem Problem 12

Internal problem ID [13788]
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 : Monday, March 31, 2025 at 08:12:02 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

\begin{align*} y &= \frac {1}{-3 x +c_1} \\ y &= \frac {1}{3 x +c_1} \\ \end{align*}

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

ode=D[y[x],x]^2==9*y[x]^4; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*y(x)**4 + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {1}{C_{1} + 3 x}, \ y{\left (x \right )} = \frac {1}{C_{1} + 3 x}\right ] \]