23.2.217 problem 223

Internal problem ID [5572]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 223
Date solved : Tuesday, September 30, 2025 at 01:00:18 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 49

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

\begin{align*} y &= \sqrt {2 a x +c_1} \\ y &= -\sqrt {2 a x +c_1} \\ y &= \sqrt {-2 a x +c_1} \\ y &= -\sqrt {-2 a x +c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 85

ode=y[x]^2(D[y[x],x])^2==a^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {2} \sqrt {-a x+c_1}\\ y(x)&\to \sqrt {2} \sqrt {-a x+c_1}\\ y(x)&\to -\sqrt {2} \sqrt {a x+c_1}\\ y(x)&\to \sqrt {2} \sqrt {a x+c_1} \end{align*}

✓ Sympy. Time used: 0.697 (sec). Leaf size: 51

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - 2 a x}, \ y{\left (x \right )} = \sqrt {C_{1} - 2 a x}, \ y{\left (x \right )} = - \sqrt {C_{1} + 2 a x}, \ y{\left (x \right )} = \sqrt {C_{1} + 2 a x}\right ] \]