84.16.7 problem 8.16

Internal problem ID [22187]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.16
Date solved : Thursday, October 02, 2025 at 08:33:46 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.204 (sec). Leaf size: 12

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

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