58.5.25 problem 25

Internal problem ID [14619]
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 : 25
Date solved : Thursday, October 02, 2025 at 09:44:31 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 17

ode:=diff(y(x),x)+1/2*y(x)/x = x/y(x)^3; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {\frac {\sqrt {x^{4}+15}}{x}} \]

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 20

ode=D[y[x],x]+y[x]/(2*x)==x/y[x]^3; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sqrt [4]{x^4+15}}{\sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.576 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x/y(x)**3 + Derivative(y(x), x) + y(x)/(2*x),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [4]{x^{2} + \frac {15}{x^{2}}} \]