56.20.3 problem Ex 3

Internal problem ID [14198]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 33. Page 73
Problem number : Ex 3
Date solved : Thursday, October 02, 2025 at 09:26:39 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 19

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

\begin{align*} y &= -x^{{3}/{2}}+c_1 \\ y &= x^{{3}/{2}}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to -x^{3/2}+c_1\\ y(x)&\to x^{3/2}+c_1 \end{align*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 17

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

\[ \left [ y{\left (x \right )} = C_{1} - x^{\frac {3}{2}}, \ y{\left (x \right )} = C_{1} + x^{\frac {3}{2}}\right ] \]