64.5.26 problem 26

Internal problem ID [13268]
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 : 26
Date solved : Monday, March 31, 2025 at 07:44:27 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x y^{\prime }+y&=\left (x y\right )^{{3}/{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Maple. Time used: 0.153 (sec). Leaf size: 9

ode:=x*diff(y(x),x)+y(x) = (x*y(x))^(3/2); 
ic:=y(1) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {4}{x^{3}} \]

✓ Mathematica. Time used: 0.267 (sec). Leaf size: 24

ode=x*D[y[x],x]+y[x]==(x*y[x])^(3/2); 
ic={y[1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {4}{x^3} \\ y(x)\to \frac {4}{(x-2)^2 x} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - (x*y(x))**(3/2) + y(x),0) 
ics = {y(1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - ((x*y(x))**(3/2) - y(x))/x cannot be solved by the factorable group method