29.31.27 problem 927

Internal problem ID [5506]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 927
Date solved : Tuesday, March 04, 2025 at 09:50:19 PM
CAS classification : [_quadrature]

\begin{align*} x^{3} {y^{\prime }}^{2}&=a \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 37

ode:=x^3*diff(y(x),x)^2 = a; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \frac {c_{1} x -2 \sqrt {a x}}{x} \\ y \left (x \right ) &= \frac {c_{1} x +2 \sqrt {a x}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 39

ode=x^3 (D[y[x],x])^2==a; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.252 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a + x**3*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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