58.5.2 problem 2

Internal problem ID [14596]
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 : 2
Date solved : Thursday, October 02, 2025 at 09:43:47 AM
CAS classification : [_linear]

\begin{align*} x^{4} y^{\prime }+2 x^{3} y&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \frac {c_1 x -1}{x^{3}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to \frac {-1+c_1 x}{x^3} \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1} x - 1}{x^{3}} \]