88.9.13 problem 13

Internal problem ID [24033]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 48
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:54:48 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 74

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

\begin{align*} y &= \frac {\left (9 x^{9}+27 c_1 \right )^{{1}/{3}}}{3 x^{2}} \\ y &= -\frac {\left (9 x^{9}+27 c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{6 x^{2}} \\ y &= \frac {\left (9 x^{9}+27 c_1 \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{6 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 78

ode=D[y[x],{x,1}]+2/x*y[x]==x^2*y[x]^(-2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{x^9+3 c_1}}{x^2}\\ y(x)&\to \frac {\sqrt [3]{\frac {x^9}{3}+c_1}}{x^2}\\ y(x)&\to \frac {(-1)^{2/3} \sqrt [3]{\frac {x^9}{3}+c_1}}{x^2} \end{align*}

✓ Sympy. Time used: 0.608 (sec). Leaf size: 80

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

\[ \left [ y{\left (x \right )} = \frac {3^{\frac {2}{3}} \sqrt [3]{\frac {C_{1}}{x^{6}} + x^{3}}}{3}, \ y{\left (x \right )} = \frac {\left (- 3^{\frac {2}{3}} - 3 \sqrt [6]{3} i\right ) \sqrt [3]{\frac {C_{1}}{x^{6}} + x^{3}}}{6}, \ y{\left (x \right )} = \frac {\left (- 3^{\frac {2}{3}} + 3 \sqrt [6]{3} i\right ) \sqrt [3]{\frac {C_{1}}{x^{6}} + x^{3}}}{6}\right ] \]