82.13.2 problem Ex. 2

Internal problem ID [18723]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 32
Problem number : Ex. 2
Date solved : Thursday, March 13, 2025 at 12:41:49 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-a \,x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 31

ode:=diff(y(x),x)^2-a*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \frac {2 x^{2} \sqrt {a x}}{5}+c_{1} \\ y \left (x \right ) &= -\frac {2 x^{2} \sqrt {a x}}{5}+c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 43

ode=D[y[x],x]^2-a*x^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {2}{5} \sqrt {a} x^{5/2}+c_1 \\ y(x)\to \frac {2}{5} \sqrt {a} x^{5/2}+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.459 (sec). Leaf size: 34

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)
 

\[ \left [ y{\left (x \right )} = C_{1} - \frac {2 \sqrt {a} x^{\frac {5}{2}}}{5}, \ y{\left (x \right )} = C_{1} + \frac {2 \sqrt {a} x^{\frac {5}{2}}}{5}\right ] \]