36.2.10 problem 10

Internal problem ID [6303]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 10
Date solved : Wednesday, March 05, 2025 at 12:33:25 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 15

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

\[ y(x)\to \frac {-1+c_1 x}{x^3} \]

✓ Sympy. Time used: 0.192 (sec). Leaf size: 10

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

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