7.7.14 problem 14

Internal problem ID [192]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 14
Date solved : Saturday, March 29, 2025 at 04:39:09 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 28

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

\begin{align*} y &= \frac {x}{\sqrt {2 \ln \left (x \right )+c_1}} \\ y &= -\frac {x}{\sqrt {2 \ln \left (x \right )+c_1}} \\ \end{align*}

✓ Mathematica. Time used: 6.96 (sec). Leaf size: 86

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

\begin{align*} y(x)\to -\frac {i e^x \sqrt {x}}{\sqrt {-4 x \operatorname {ExpIntegralEi}(2 x)+2 e^{2 x}+c_1 (-x)}} \\ y(x)\to \frac {i e^x \sqrt {x}}{\sqrt {-4 x \operatorname {ExpIntegralEi}(2 x)+2 e^{2 x}+c_1 (-x)}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.643 (sec). Leaf size: 32

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

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