12.2.19 problem 19

Internal problem ID [1555]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 19
Date solved : Saturday, March 29, 2025 at 10:58:53 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = \frac {\frac {x^{2}}{2}+2 \ln \left (x \right )+c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 22

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

\[ y(x)\to \frac {2 \log (x)}{x^2}+\frac {c_1}{x^2}+\frac {1}{2} \]

✓ Sympy. Time used: 0.219 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{2}}{2} + 2 \log {\left (x \right )}}{x^{2}} \]