71.1.22 problem 36

Internal problem ID [14260]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 36
Date solved : Monday, March 31, 2025 at 12:14:32 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}-9 x y&=0 \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 69

ode:=diff(y(x),x)^2-9*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= x^{3}+2 \sqrt {c_1 x}\, x +c_1 \\ y &= x^{3}-2 \sqrt {c_1 x}\, x +c_1 \\ y &= x^{3}-2 \sqrt {c_1 x}\, x +c_1 \\ y &= x^{3}+2 \sqrt {c_1 x}\, x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 46

ode=(D[y[x],x])^2-9*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (-2 x^{3/2}+c_1\right ){}^2 \\ y(x)\to \frac {1}{4} \left (2 x^{3/2}+c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.727 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} - C_{1} \sqrt {x^{3}} + x^{3} \]