58.5.17 problem 17

Internal problem ID [14611]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:44:16 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 92

ode:=diff(y(x),x)+(4*y(x)-8/y(x)^3)*x = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \left (2 \,{\mathrm e}^{8 x^{2}}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ y &= -\left (2 \,{\mathrm e}^{8 x^{2}}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ y &= -i \left (2 \,{\mathrm e}^{8 x^{2}}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ y &= i \left (2 \,{\mathrm e}^{8 x^{2}}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 1.807 (sec). Leaf size: 145

ode=D[y[x],x]+(4*y[x]-8/y[x]^3)*x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt [4]{2+e^{-8 x^2+4 c_1}}\\ y(x)&\to -i \sqrt [4]{2+e^{-8 x^2+4 c_1}}\\ y(x)&\to i \sqrt [4]{2+e^{-8 x^2+4 c_1}}\\ y(x)&\to \sqrt [4]{2+e^{-8 x^2+4 c_1}}\\ y(x)&\to -\sqrt [4]{2}\\ y(x)&\to -i \sqrt [4]{2}\\ y(x)&\to i \sqrt [4]{2}\\ y(x)&\to \sqrt [4]{2} \end{align*}

✓ Sympy. Time used: 1.435 (sec). Leaf size: 68

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(4*y(x) - 8/y(x)**3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{C_{1} e^{- 8 x^{2}} + 2}, \ y{\left (x \right )} = i \sqrt [4]{C_{1} e^{- 8 x^{2}} + 2}, \ y{\left (x \right )} = - \sqrt [4]{C_{1} e^{- 8 x^{2}} + 2}, \ y{\left (x \right )} = \sqrt [4]{C_{1} e^{- 8 x^{2}} + 2}\right ] \]